record_id string | paper_system_number int64 | task_type string | problem_name string | tier string | dimension int64 | time_domain string | dynamics string | specification_latex string | citations list | problem_json string | executable_record_json string | descriptive_record_json string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
DCB-LIT-P1-001 | 1 | stability | Stability certification | literature | 2 | continuous | dx1/dt = -((1)/(2))*tan(((pi*x1)/(2))+((pi)/(4)))+x2+((1)/(2)), dx2/dt = x1-((1)/(2))*tan(((pi*x2)/(2))+((pi)/(4)))+((1)/(2)) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} -\dfrac{1}{2}\tan\left(\dfrac{\pi x_1}{2} + \dfrac{\pi}{4}\right) + x_2 + \dfrac{1}{2}\\[1.5ex] x_1 - \dfrac{1}{2}\tan\left(\dfrac{\pi x_2}{2} + \dfrac{\pi}{4}\right) + \dfrac{1}{2} \end{pmatrix}. \] | [
"khalil2002nonlinear"
] | {"problem_id":"dcb_lit_p1_001","task_type":"stability","name":"DynaCertBench System 001 · DCB-LIT-P1-001 · Exercise~4.30, \\cite{khalil2002nonlinear}","dynamics":"dx1/dt = -((1)/(2))*tan(((pi*x1)/(2))+((pi)/(4)))+x2+((1)/(2)), dx2/dt = x1-((1)/(2))*tan(((pi*x2)/(2))+((pi)/(4)))+((1)/(2))","source":"paper System 1; cano... | {"record_id":"DCB-LIT-P1-001","problem":{"problem_id":"dcb_lit_p1_001","task_type":"stability","name":"DynaCertBench System 001 · DCB-LIT-P1-001 · Exercise~4.30, \\cite{khalil2002nonlinear}","dynamics":"dx1/dt = -((1)/(2))*tan(((pi*x1)/(2))+((pi)/(4)))+x2+((1)/(2)), dx2/dt = x1-((1)/(2))*tan(((pi*x2)/(2))+((pi)/(4)))+(... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x}\\in\\m... |
DCB-LIT-P1-002 | 2 | stability | Stability certification | literature | 2 | continuous | dx1/dt = -x1+x1*x2, dx2/dt = -x2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} -x_1+x_1x_2\\ -x_2 \end{pmatrix}. \] | [
"abate2021fossil"
] | {"problem_id":"dcb_lit_p1_002","task_type":"stability","name":"DynaCertBench System 002 · DCB-LIT-P1-002 · Table~1 row~1 (NonPoly0), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1+x1*x2, dx2/dt = -x2","source":"paper System 2; canonical record DCB-LIT-P1-002","assumptions":["Deterministically normalized from canonic... | {"record_id":"DCB-LIT-P1-002","problem":{"problem_id":"dcb_lit_p1_002","task_type":"stability","name":"DynaCertBench System 002 · DCB-LIT-P1-002 · Table~1 row~1 (NonPoly0), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1+x1*x2, dx2/dt = -x2","source":"paper System 2; canonical record DCB-LIT-P1-002","assumptions":["D... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x}\\in\\m... |
DCB-LIT-P1-003 | 3 | stability | Stability certification | literature | 2 | continuous | dx1/dt = -x1+2*x1**2*x2, dx2/dt = -x2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} -x_1+2x_1^2x_2\\ -x_2 \end{pmatrix}. \] | [
"abate2021fossil"
] | {"problem_id":"dcb_lit_p1_003","task_type":"stability","name":"DynaCertBench System 003 · DCB-LIT-P1-003 · Table~1 row~2 (NonPoly1), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1+2*x1**2*x2, dx2/dt = -x2","source":"paper System 3; canonical record DCB-LIT-P1-003","assumptions":["Deterministically normalized from ca... | {"record_id":"DCB-LIT-P1-003","problem":{"problem_id":"dcb_lit_p1_003","task_type":"stability","name":"DynaCertBench System 003 · DCB-LIT-P1-003 · Table~1 row~2 (NonPoly1), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1+2*x1**2*x2, dx2/dt = -x2","source":"paper System 3; canonical record DCB-LIT-P1-003","assumptions... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x}\\in\\m... |
DCB-LIT-P1-004 | 4 | stability | Stability certification | literature | 3 | continuous | dx1/dt = -x1, dx2/dt = -2*x2+0.1*x1*x2**2+x3, dx3/dt = -x3-1.5*x2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3 \end{pmatrix} = \begin{pmatrix} -x_1\\ -2x_2+0.1x_1x_2^2+x_3\\ -x_3-1.5x_2 \end{pmatrix}. \] | [
"abate2021fossil"
] | {"problem_id":"dcb_lit_p1_004","task_type":"stability","name":"DynaCertBench System 004 · DCB-LIT-P1-004 · Table~1 row~3 (NonPoly2), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1, dx2/dt = -2*x2+0.1*x1*x2**2+x3, dx3/dt = -x3-1.5*x2","source":"paper System 4; canonical record DCB-LIT-P1-004","assumptions":["Determin... | {"record_id":"DCB-LIT-P1-004","problem":{"problem_id":"dcb_lit_p1_004","task_type":"stability","name":"DynaCertBench System 004 · DCB-LIT-P1-004 · Table~1 row~3 (NonPoly2), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1, dx2/dt = -2*x2+0.1*x1*x2**2+x3, dx3/dt = -x3-1.5*x2","source":"paper System 4; canonical record ... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x}\\in\... |
DCB-LIT-P1-005 | 5 | stability | Stability certification | literature | 3 | continuous | dx1/dt = -3*x1-0.1*x1*x2**3, dx2/dt = -x2+x3, dx3/dt = -x3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3 \end{pmatrix} = \begin{pmatrix} -3x_1-0.1x_1x_2^3\\ -x_2+x_3\\ -x_3 \end{pmatrix}. \] | [
"abate2021fossil"
] | {"problem_id":"dcb_lit_p1_005","task_type":"stability","name":"DynaCertBench System 005 · DCB-LIT-P1-005 · Table~1 row~4 (NonPoly3), \\cite{abate2021fossil}","dynamics":"dx1/dt = -3*x1-0.1*x1*x2**3, dx2/dt = -x2+x3, dx3/dt = -x3","source":"paper System 5; canonical record DCB-LIT-P1-005","assumptions":["Deterministical... | {"record_id":"DCB-LIT-P1-005","problem":{"problem_id":"dcb_lit_p1_005","task_type":"stability","name":"DynaCertBench System 005 · DCB-LIT-P1-005 · Table~1 row~4 (NonPoly3), \\cite{abate2021fossil}","dynamics":"dx1/dt = -3*x1-0.1*x1*x2**3, dx2/dt = -x2+x3, dx3/dt = -x3","source":"paper System 5; canonical record DCB-LIT... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x}\\in\... |
DCB-LIT-P1-006 | 6 | stability | Stability certification | literature | 3 | continuous | dx1/dt = -x1**3-x1*x3**2, dx2/dt = -x2-x1**2*x2, dx3/dt = -x3+3*x1**2*x3-3*x3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3 \end{pmatrix} = \begin{pmatrix} -x_1^3-x_1x_3^2\\ -x_2-x_1^2x_2\\ -x_3+3x_1^2x_3-3x_3 \end{pmatrix}. \] | [
"abate2021fossil"
] | {"problem_id":"dcb_lit_p1_006","task_type":"stability","name":"DynaCertBench System 006 · DCB-LIT-P1-006 · Table~1 row~5 (Poly1), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1**3-x1*x3**2, dx2/dt = -x2-x1**2*x2, dx3/dt = -x3+3*x1**2*x3-3*x3","source":"paper System 6; canonical record DCB-LIT-P1-006","assumptions":[... | {"record_id":"DCB-LIT-P1-006","problem":{"problem_id":"dcb_lit_p1_006","task_type":"stability","name":"DynaCertBench System 006 · DCB-LIT-P1-006 · Table~1 row~5 (Poly1), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1**3-x1*x3**2, dx2/dt = -x2-x1**2*x2, dx3/dt = -x3+3*x1**2*x3-3*x3","source":"paper System 6; canonica... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x}\\in\... |
DCB-LIT-P1-007 | 7 | stability | Stability certification | literature | 2 | continuous | dx1/dt = -x1**3+x2, dx2/dt = -x1-x2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} -x_1^3+x_2\\ -x_1-x_2 \end{pmatrix}. \] | [
"abate2021fossil"
] | {"problem_id":"dcb_lit_p1_007","task_type":"stability","name":"DynaCertBench System 007 · DCB-LIT-P1-007 · Table~1 row~6 (Poly2), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1**3+x2, dx2/dt = -x1-x2","source":"paper System 7; canonical record DCB-LIT-P1-007","assumptions":["Deterministically normalized from canonic... | {"record_id":"DCB-LIT-P1-007","problem":{"problem_id":"dcb_lit_p1_007","task_type":"stability","name":"DynaCertBench System 007 · DCB-LIT-P1-007 · Table~1 row~6 (Poly2), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1**3+x2, dx2/dt = -x1-x2","source":"paper System 7; canonical record DCB-LIT-P1-007","assumptions":["D... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x}\\in\\m... |
DCB-LIT-P1-008 | 8 | stability | Stability certification | literature | 2 | continuous | dx1/dt = -x1**3-x2**2, dx2/dt = x1*x2-x2**3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} -x_1^3-x_2^2\\ x_1x_2-x_2^3 \end{pmatrix}. \] | [
"abate2021fossil"
] | {"problem_id":"dcb_lit_p1_008","task_type":"stability","name":"DynaCertBench System 008 · DCB-LIT-P1-008 · Table~1 row~7 (Poly3), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1**3-x2**2, dx2/dt = x1*x2-x2**3","source":"paper System 8; canonical record DCB-LIT-P1-008","assumptions":["Deterministically normalized from... | {"record_id":"DCB-LIT-P1-008","problem":{"problem_id":"dcb_lit_p1_008","task_type":"stability","name":"DynaCertBench System 008 · DCB-LIT-P1-008 · Table~1 row~7 (Poly3), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1**3-x2**2, dx2/dt = x1*x2-x2**3","source":"paper System 8; canonical record DCB-LIT-P1-008","assumpti... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x}\\in\\m... |
DCB-LIT-P1-009 | 9 | stability | Stability certification | literature | 2 | continuous | dx1/dt = -x1-1.5*x1**2*x2**3, dx2/dt = -x2**3+0.5*x1**3*x2**2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} -x_1-1.5x_1^2x_2^3\\ -x_2^3+0.5x_1^3x_2^2 \end{pmatrix}. \] | [
"abate2021fossil"
] | {"problem_id":"dcb_lit_p1_009","task_type":"stability","name":"DynaCertBench System 009 · DCB-LIT-P1-009 · Table~1 row~8 (Poly4), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1-1.5*x1**2*x2**3, dx2/dt = -x2**3+0.5*x1**3*x2**2","source":"paper System 9; canonical record DCB-LIT-P1-009","assumptions":["Deterministical... | {"record_id":"DCB-LIT-P1-009","problem":{"problem_id":"dcb_lit_p1_009","task_type":"stability","name":"DynaCertBench System 009 · DCB-LIT-P1-009 · Table~1 row~8 (Poly4), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1-1.5*x1**2*x2**3, dx2/dt = -x2**3+0.5*x1**3*x2**2","source":"paper System 9; canonical record DCB-LIT... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x}\\in\\m... |
DCB-LIT-P1-010 | 10 | stability | Stability certification | literature | 2 | continuous | dx1/dt = x2+u1, dx2/dt = u2+((3/20)*(981/100)*(1/2)*sin(x1)-(1/10)*x2)/((3/20)*(1/2)**2) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} x_2+u_1\\ u_2+\dfrac{mgL\sin(x_1)-bx_2}{mL^2} \end{pmatrix}, \] where $m=0.15$, $g=9.81$, $L=0.5$, and $b=0.1$. | [
"edwards2024fossil"
] | {"problem_id":"dcb_lit_p1_010","task_type":"stability","name":"DynaCertBench System 010 · DCB-LIT-P1-010 · Table~4 \\#2 (SineModel), \\cite{edwards2024fossil}","dynamics":"dx1/dt = x2+u1, dx2/dt = u2+((3/20)*(981/100)*(1/2)*sin(x1)-(1/10)*x2)/((3/20)*(1/2)**2)","source":"paper System 10; canonical record DCB-LIT-P1-010... | {"record_id":"DCB-LIT-P1-010","problem":{"problem_id":"dcb_lit_p1_010","task_type":"stability","name":"DynaCertBench System 010 · DCB-LIT-P1-010 · Table~4 \\#2 (SineModel), \\cite{edwards2024fossil}","dynamics":"dx1/dt = x2+u1, dx2/dt = u2+((3/20)*(981/100)*(1/2)*sin(x1)-(1/10)*x2)/((3/20)*(1/2)**2)","source":"paper Sy... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x}\\in\\m... |
DCB-LIT-P1-011 | 11 | stability | Stability certification | literature | 2 | discrete | x1[k+1] = 0.687*x1+0.558*x2-0.0001*x1*x2, x2[k+1] = -0.292*x1+0.773*x2 | The discrete-time transition map is: \[ \mathbf{x}^{+} = F(\mathbf{x}) = \begin{pmatrix} 0.687x_1+0.558x_2-0.0001x_1x_2\\ -0.292x_1+0.773x_2 \end{pmatrix}. \] | [
"edwards2024fossil"
] | {"problem_id":"dcb_lit_p1_011","task_type":"stability","name":"DynaCertBench System 011 · DCB-LIT-P1-011 · Table~4 \\#14 (DTAhmadi2), \\cite{edwards2024fossil}","dynamics":"x1[k+1] = 0.687*x1+0.558*x2-0.0001*x1*x2, x2[k+1] = -0.292*x1+0.773*x2","source":"paper System 11; canonical record DCB-LIT-P1-011","assumptions":[... | {"record_id":"DCB-LIT-P1-011","problem":{"problem_id":"dcb_lit_p1_011","task_type":"stability","name":"DynaCertBench System 011 · DCB-LIT-P1-011 · Table~4 \\#14 (DTAhmadi2), \\cite{edwards2024fossil}","dynamics":"x1[k+1] = 0.687*x1+0.558*x2-0.0001*x1*x2, x2[k+1] = -0.292*x1+0.773*x2","source":"paper System 11; canonica... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x}\\in\\m... |
DCB-LIT-P1-012 | 12 | stability | Stability certification | literature | 2 | discrete | x1[k+1] = 0.3*x1+u1, x2[k+1] = -x1+0.5*x2+((7)/(18))*x1**2+u2 | The discrete-time transition map is: \[ \mathbf{x}^{+} = F(\mathbf{x},\mathbf{u}) = \begin{pmatrix} 0.3x_1+u_1\\ -x_1+0.5x_2+\dfrac{7}{18}x_1^2+u_2 \end{pmatrix}. \] | [
"edwards2024fossil"
] | {"problem_id":"dcb_lit_p1_012","task_type":"stability","name":"DynaCertBench System 012 · DCB-LIT-P1-012 · Table~4 \\#15 (DTAhmadi), \\cite{edwards2024fossil}","dynamics":"x1[k+1] = 0.3*x1+u1, x2[k+1] = -x1+0.5*x2+((7)/(18))*x1**2+u2","source":"paper System 12; canonical record DCB-LIT-P1-012","assumptions":["Determini... | {"record_id":"DCB-LIT-P1-012","problem":{"problem_id":"dcb_lit_p1_012","task_type":"stability","name":"DynaCertBench System 012 · DCB-LIT-P1-012 · Table~4 \\#15 (DTAhmadi), \\cite{edwards2024fossil}","dynamics":"x1[k+1] = 0.3*x1+u1, x2[k+1] = -x1+0.5*x2+((7)/(18))*x1**2+u2","source":"paper System 12; canonical record D... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x}\\in\\m... |
DCB-LIT-P1-013 | 13 | stability | Stability certification | literature | 3 | continuous | dx1/dt = -3*x1**3+3*x1*x3-9*x1, dx2/dt = -x1**3-5*x2+5*x3**3, dx3/dt = -9*x3**3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3 \end{pmatrix} = \begin{pmatrix} -3x_1^3+3x_1x_3-9x_1\\ -x_1^3-5x_2+5x_3^3\\ -9x_3^3 \end{pmatrix}. \] | [
"zou2025analytical"
] | {"problem_id":"dcb_lit_p1_013","task_type":"stability","name":"DynaCertBench System 013 · DCB-LIT-P1-013 · Table~1 row~4, \\cite{zou2025analytical}","dynamics":"dx1/dt = -3*x1**3+3*x1*x3-9*x1, dx2/dt = -x1**3-5*x2+5*x3**3, dx3/dt = -9*x3**3","source":"paper System 13; canonical record DCB-LIT-P1-013","assumptions":["De... | {"record_id":"DCB-LIT-P1-013","problem":{"problem_id":"dcb_lit_p1_013","task_type":"stability","name":"DynaCertBench System 013 · DCB-LIT-P1-013 · Table~1 row~4, \\cite{zou2025analytical}","dynamics":"dx1/dt = -3*x1**3+3*x1*x3-9*x1, dx2/dt = -x1**3-5*x2+5*x3**3, dx3/dt = -9*x3**3","source":"paper System 13; canonical r... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x}\\in\... |
DCB-LIT-P1-014 | 14 | stability | Stability certification | literature | 3 | continuous | dx1/dt = x2, dx2/dt = -sin(x1)*cos(x1)-x2-sin(x3)*cos(x3), dx3/dt = x2-x3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3 \end{pmatrix} = \begin{pmatrix} x_2\\ -\sin(x_1)\cos(x_1)-x_2-\sin(x_3)\cos(x_3)\\ x_2-x_3 \end{pmatrix}. \] | [
"zou2025analytical"
] | {"problem_id":"dcb_lit_p1_014","task_type":"stability","name":"DynaCertBench System 014 · DCB-LIT-P1-014 · Table~1 row~5, \\cite{zou2025analytical}","dynamics":"dx1/dt = x2, dx2/dt = -sin(x1)*cos(x1)-x2-sin(x3)*cos(x3), dx3/dt = x2-x3","source":"paper System 14; canonical record DCB-LIT-P1-014","assumptions":["Determin... | {"record_id":"DCB-LIT-P1-014","problem":{"problem_id":"dcb_lit_p1_014","task_type":"stability","name":"DynaCertBench System 014 · DCB-LIT-P1-014 · Table~1 row~5, \\cite{zou2025analytical}","dynamics":"dx1/dt = x2, dx2/dt = -sin(x1)*cos(x1)-x2-sin(x3)*cos(x3), dx3/dt = x2-x3","source":"paper System 14; canonical record ... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x}\\in\... |
DCB-LIT-P1-015 | 15 | stability | Stability certification | literature | 4 | continuous | dq/dt = w1-w2, dw1/dt = (1/2)*(-1-2*w1-sin(q)+cos(q)), dw2/dt = (1/2)*(-1-2*w2+sin(q)+cos(q)) | The source system is expressed in the center-of-inertia coordinates $(\delta_1,\delta_2,\omega_1,\omega_2)$, which satisfy $\delta_1+\delta_2=0$. We therefore remove the redundant common-angle coordinate and define $q:=\delta_1-\delta_2, \delta_1=\frac{q}{2}, \delta_2=-\frac{q}{2}$. Let $\mathbf{x}=(q,\omega_1,\omega_2... | [
"zou2025analytical"
] | {"problem_id":"dcb_lit_p1_015","task_type":"stability","name":"DynaCertBench System 015 · DCB-LIT-P1-015 · Table~1 row~6, \\cite{zou2025analytical}","dynamics":"dq/dt = w1-w2, dw1/dt = (1/2)*(-1-2*w1-sin(q)+cos(q)), dw2/dt = (1/2)*(-1-2*w2+sin(q)+cos(q))","source":"paper System 15; canonical record DCB-LIT-P1-015","ass... | {"record_id":"DCB-LIT-P1-015","problem":{"problem_id":"dcb_lit_p1_015","task_type":"stability","name":"DynaCertBench System 015 · DCB-LIT-P1-015 · Table~1 row~6, \\cite{zou2025analytical}","dynamics":"dq/dt = w1-w2, dw1/dt = (1/2)*(-1-2*w1-sin(q)+cos(q)), dw2/dt = (1/2)*(-1-2*w2+sin(q)+cos(q))","source":"paper System 1... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0,0)$","Original $ \\mathcal{N} = \\left\\{ (q,\\o... |
DCB-LIT-P1-016 | 16 | stability | Stability certification | literature | 6 | continuous | dx1/dt = -x1+0.5*x2-0.1*x5**2, dx2/dt = -0.5*x1-x2, dx3/dt = -x3+0.5*x4-0.1*x1**2, dx4/dt = -0.5*x3-x4, dx5/dt = -x5+0.5*x6, dx6/dt = -0.5*x5-x6+0.1*x2**2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4\\ \dot{x}_5\\ \dot{x}_6 \end{pmatrix} = \begin{pmatrix} -x_1+0.5x_2-0.1x_5^2\\ -0.5x_1-x_2\\ -x_3+0.5x_4-0.1x_1^2\\ -0.5x_3-x_4\\ -x_5+0.5x_6\\ -0.5x_5-x_6+0.1x_2^2 \end{pmatrix}. \] | [
"zou2025analytical"
] | {"problem_id":"dcb_lit_p1_016","task_type":"stability","name":"DynaCertBench System 016 · DCB-LIT-P1-016 · Table~1 row~7, \\cite{zou2025analytical}","dynamics":"dx1/dt = -x1+0.5*x2-0.1*x5**2, dx2/dt = -0.5*x1-x2, dx3/dt = -x3+0.5*x4-0.1*x1**2, dx4/dt = -0.5*x3-x4, dx5/dt = -x5+0.5*x6, dx6/dt = -0.5*x5-x6+0.1*x2**2","so... | {"record_id":"DCB-LIT-P1-016","problem":{"problem_id":"dcb_lit_p1_016","task_type":"stability","name":"DynaCertBench System 016 · DCB-LIT-P1-016 · Table~1 row~7, \\cite{zou2025analytical}","dynamics":"dx1/dt = -x1+0.5*x2-0.1*x5**2, dx2/dt = -0.5*x1-x2, dx3/dt = -x3+0.5*x4-0.1*x1**2, dx4/dt = -0.5*x3-x4, dx5/dt = -x5+0.... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0,0,0,0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x... |
DCB-LIT-P1-017 | 17 | stability | Stability certification | literature | 6 | continuous | dx1/dt = x2, dx2/dt = -((3)/(2))*x6*x4-2*x1-((5)/(2))*x2-((1)/(2))*x4*sin(x2)*cos(x4), dx3/dt = x4, dx4/dt = ((3)/(2))*x6*x2-2*x3-10*x4+((1)/(2))*x2*sin(x2)*cos(x4), dx5/dt = x6, dx6/dt = -5*x5-((4)/(5))*x6 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4\\ \dot{x}_5\\ \dot{x}_6 \end{pmatrix} = \begin{pmatrix} x_2\\ -\tfrac32x_6x_4-2x_1-\tfrac52x_2-\tfrac12x_4\sin(x_2)\cos(x_4)\\ x_4\\ \tfrac32x_6x_2-2x_3-10x_4+\tfrac12x_2\sin(x_2)\cos(x_4)\\ x_6\\ -5x_5-\tfrac4... | [
"zou2025analytical"
] | {"problem_id":"dcb_lit_p1_017","task_type":"stability","name":"DynaCertBench System 017 · DCB-LIT-P1-017 · Table~1 row~8, \\cite{zou2025analytical}","dynamics":"dx1/dt = x2, dx2/dt = -((3)/(2))*x6*x4-2*x1-((5)/(2))*x2-((1)/(2))*x4*sin(x2)*cos(x4), dx3/dt = x4, dx4/dt = ((3)/(2))*x6*x2-2*x3-10*x4+((1)/(2))*x2*sin(x2)*co... | {"record_id":"DCB-LIT-P1-017","problem":{"problem_id":"dcb_lit_p1_017","task_type":"stability","name":"DynaCertBench System 017 · DCB-LIT-P1-017 · Table~1 row~8, \\cite{zou2025analytical}","dynamics":"dx1/dt = x2, dx2/dt = -((3)/(2))*x6*x4-2*x1-((5)/(2))*x2-((1)/(2))*x4*sin(x2)*cos(x4), dx3/dt = x4, dx4/dt = ((3)/(2))*... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0,0,0,0,0)$","Original $\\mathcal{N}=\\{\\mathbf{x... |
DCB-LIT-P1-018 | 18 | stability | Stability certification | literature | 6 | continuous | dd1/dt = w1-(w1+w2+w3)/3, dd2/dt = w2-(w1+w2+w3)/3, dw1/dt = -w1-(1/2)*(sin(d1-d2)+sin(2*d1+d2)), dw2/dt = -w2-(1/2)*(sin(d2-d1)+sin(d1+2*d2)), dw3/dt = -w3+(1/2)*(sin(2*d1+d2)+sin(d1+2*d2)) | The source system is expressed in the center-of-inertia coordinates $(\delta_1,\delta_2,\delta_3,\omega_1,\omega_2,\omega_3)$, which satisfy $\delta_1+\delta_2+\delta_3=0$. We therefore remove the redundant common-angle coordinate and define $\delta_3:=-(\delta_1+\delta_2)$ and $\bar{\omega}:=\frac13(\omega_1+\omega_2+... | [
"zou2025analytical"
] | {"problem_id":"dcb_lit_p1_018","task_type":"stability","name":"DynaCertBench System 018 · DCB-LIT-P1-018 · Table~1 row~9, \\cite{zou2025analytical}","dynamics":"dd1/dt = w1-(w1+w2+w3)/3, dd2/dt = w2-(w1+w2+w3)/3, dw1/dt = -w1-(1/2)*(sin(d1-d2)+sin(2*d1+d2)), dw2/dt = -w2-(1/2)*(sin(d2-d1)+sin(d1+2*d2)), dw3/dt = -w3+(1... | {"record_id":"DCB-LIT-P1-018","problem":{"problem_id":"dcb_lit_p1_018","task_type":"stability","name":"DynaCertBench System 018 · DCB-LIT-P1-018 · Table~1 row~9, \\cite{zou2025analytical}","dynamics":"dd1/dt = w1-(w1+w2+w3)/3, dd2/dt = w2-(w1+w2+w3)/3, dw1/dt = -w1-(1/2)*(sin(d1-d2)+sin(2*d1+d2)), dw2/dt = -w2-(1/2)*(s... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0,0,0,0)$","Original $\\mathcal{N} = \\{(\\delta_1... |
DCB-LIT-P1-019 | 19 | stability | Stability certification | literature | 9 | continuous | dx1/dt = -x1+0.5*x2-0.1*x5**2, dx2/dt = -0.5*x1-x2+0.1*x8, dx3/dt = -x3+0.5*x4-0.1*x1**2, dx4/dt = -0.5*x3-x4, dx5/dt = -x5+0.5*x6, dx6/dt = -0.5*x5-x6+0.1*x2**2, dx7/dt = x8, dx8/dt = -sin(x7)*cos(x7)-x8-sin(x9)*cos(x9)-0.1*x2, dx9/dt = x8-x9 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4\\ \dot{x}_5\\ \dot{x}_6\\ \dot{x}_7\\ \dot{x}_8\\ \dot{x}_9 \end{pmatrix} = \begin{pmatrix} -x_1+0.5x_2-0.1x_5^2\\ -0.5x_1-x_2+0.1x_8\\ -x_3+0.5x_4-0.1x_1^2\\ -0.5x_3-x_4\\ -x_5+0.5x_6\\ -0.5x_5-x_6+0.1x_2^2\\ ... | [
"zou2025analytical"
] | {"problem_id":"dcb_lit_p1_019","task_type":"stability","name":"DynaCertBench System 019 · DCB-LIT-P1-019 · Table~1 row~10, \\cite{zou2025analytical}","dynamics":"dx1/dt = -x1+0.5*x2-0.1*x5**2, dx2/dt = -0.5*x1-x2+0.1*x8, dx3/dt = -x3+0.5*x4-0.1*x1**2, dx4/dt = -0.5*x3-x4, dx5/dt = -x5+0.5*x6, dx6/dt = -0.5*x5-x6+0.1*x2... | {"record_id":"DCB-LIT-P1-019","problem":{"problem_id":"dcb_lit_p1_019","task_type":"stability","name":"DynaCertBench System 019 · DCB-LIT-P1-019 · Table~1 row~10, \\cite{zou2025analytical}","dynamics":"dx1/dt = -x1+0.5*x2-0.1*x5**2, dx2/dt = -0.5*x1-x2+0.1*x8, dx3/dt = -x3+0.5*x4-0.1*x1**2, dx4/dt = -0.5*x3-x4, dx5/dt ... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0,0,0,0,0,0,0,0)$","Original $\\mathcal{N}=\\{\\ma... |
DCB-LIT-P1-020 | 20 | stability | Stability certification | literature | 3 | continuous | dx1/dt = -8*x1*x2**2-10*x2**4, dx2/dt = -8*x2**3+3*x2**2-8*x2, dx3/dt = -x3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3 \end{pmatrix} = \begin{pmatrix} -8x_1x_2^2-10x_2^4\\ -8x_2^3+3x_2^2-8x_2\\ -x_3 \end{pmatrix}. \] | [
"zou2025analytical"
] | {"problem_id":"dcb_lit_p1_020","task_type":"stability","name":"DynaCertBench System 020 · DCB-LIT-P1-020 · Appendix Table~6, \\cite{zou2025analytical}","dynamics":"dx1/dt = -8*x1*x2**2-10*x2**4, dx2/dt = -8*x2**3+3*x2**2-8*x2, dx3/dt = -x3","source":"paper System 20; canonical record DCB-LIT-P1-020","assumptions":["Det... | {"record_id":"DCB-LIT-P1-020","problem":{"problem_id":"dcb_lit_p1_020","task_type":"stability","name":"DynaCertBench System 020 · DCB-LIT-P1-020 · Appendix Table~6, \\cite{zou2025analytical}","dynamics":"dx1/dt = -8*x1*x2**2-10*x2**4, dx2/dt = -8*x2**3+3*x2**2-8*x2, dx3/dt = -x3","source":"paper System 20; canonical re... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["Original $\\mathcal{N}=\\{\\mathbf{x}\\in\\mathbb{R}^{3}\\mid e... |
DCB-LIT-P1-021 | 21 | stability | Stability certification | literature | 2 | continuous | dx1/dt = 4*x1**3-x1**2*x2-6*x1*x2**2-x2**3, dx2/dt = x1**3+4*x1**2*x2+x1*x2**2-6*x2**3 | The vector flow field is: \[ \dot{\mathbf{x}}= \begin{pmatrix}\dot{x}\\\dot{y}\end{pmatrix} = \begin{pmatrix}4x^3-x^2y-6xy^2-y^3\\x^3+4x^2y+xy^2-6y^3\end{pmatrix}. \] | [
"liu2026globally"
] | {"problem_id":"dcb_lit_p1_021","task_type":"stability","name":"DynaCertBench System 021 · DCB-LIT-P1-021 · Main theorem, \\cite{liu2026globally}","dynamics":"dx1/dt = 4*x1**3-x1**2*x2-6*x1*x2**2-x2**3, dx2/dt = x1**3+4*x1**2*x2+x1*x2**2-6*x2**3","source":"paper System 21; canonical record DCB-LIT-P1-021","assumptions":... | {"record_id":"DCB-LIT-P1-021","problem":{"problem_id":"dcb_lit_p1_021","task_type":"stability","name":"DynaCertBench System 021 · DCB-LIT-P1-021 · Main theorem, \\cite{liu2026globally}","dynamics":"dx1/dt = 4*x1**3-x1**2*x2-6*x1*x2**2-x2**3, dx2/dt = x1**3+4*x1**2*x2+x1*x2**2-6*x2**3","source":"paper System 21; canonic... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0)$","Original $\\mathcal{N}=\\mathbb{R}^{2}$","Or... |
DCB-LIT-P2-001 | 22 | roa | Region-of-attraction verification | literature | 2 | continuous | dx1/dt = x2, dx2/dt = ((3/20)*(981/100)*(1/2)*sin(x1)+(20*tanh(-(23286329/1000000)*x1-(105411/20000)*x2))-(1/10)*x2)/((3/20)*(1/2)**2) | The closed-loop vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{\theta}\\ \dot{\omega} \end{pmatrix} = \begin{pmatrix} \omega\\ \dfrac{mg\ell\sin(\theta)+u-0.1\omega}{m\ell^2} \end{pmatrix}. \] \[ u=20\tanh(-23.286329\theta-5.27055\omega), \] where $m=0.15,\ell=0.5$ and $g=9.81$. | [
"zhou2022neural"
] | {"problem_id":"dcb_lit_p2_001","task_type":"roa","name":"DynaCertBench System 022 · DCB-LIT-P2-001 · Section~5.3 and Appendix~C.3.3, \\cite{zhou2022neural}","dynamics":"dx1/dt = x2, dx2/dt = ((3/20)*(981/100)*(1/2)*sin(x1)+(20*tanh(-(23286329/1000000)*x1-(105411/20000)*x2))-(1/10)*x2)/((3/20)*(1/2)**2)","source":"paper... | {"record_id":"DCB-LIT-P2-001","problem":{"problem_id":"dcb_lit_p2_001","task_type":"roa","name":"DynaCertBench System 022 · DCB-LIT-P2-001 · Section~5.3 and Appendix~C.3.3, \\cite{zhou2022neural}","dynamics":"dx1/dt = x2, dx2/dt = ((3/20)*(981/100)*(1/2)*sin(x1)+(20*tanh(-(23286329/1000000)*x1-(105411/20000)*x2))-(1/10... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":2,"problem_name":"Region-of-attraction verification","raw_items_latex":["$x^\\star=(0,0)$","Original $\\mathcal{N}=\\{\\mathbf... |
DCB-LIT-P2-002 | 23 | roa | Region-of-attraction verification | literature | 2 | continuous | dx1/dt = -x2, dx2/dt = x1 + (x1**2 - 1)*x2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} -x_2\\ x_1+(x_1^2-1)x_2 \end{pmatrix}. \] | [
"zhou2022neural"
] | {"problem_id":"dcb_lit_p2_002","task_type":"roa","name":"DynaCertBench System 023 · DCB-LIT-P2-002 · Section~5.1 and Appendix~C.3.1, \\cite{zhou2022neural}","dynamics":"dx1/dt = -x2, dx2/dt = x1 + (x1**2 - 1)*x2","equilibrium":[0,0],"stability_kind":"local_asymptotic","neighborhood":{"type":"ball","center":[0,0],"radiu... | {"record_id":"DCB-LIT-P2-002","problem":{"problem_id":"dcb_lit_p2_002","task_type":"roa","name":"DynaCertBench System 023 · DCB-LIT-P2-002 · Section~5.1 and Appendix~C.3.1, \\cite{zhou2022neural}","dynamics":"dx1/dt = -x2, dx2/dt = x1 + (x1**2 - 1)*x2","equilibrium":[0,0],"stability_kind":"local_asymptotic","neighborho... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":2,"problem_name":"Region-of-attraction verification","raw_items_latex":["$x^\\star=(0,0)$","Original $\\mathcal{N}=\\{\\mathbf... |
DCB-LIT-P2-003 | 24 | roa | Region-of-attraction verification | literature | 1 | continuous | dx/dt = -x + x**3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x} \end{pmatrix} = \begin{pmatrix} -x+x^3 \end{pmatrix}. \] | [
"liu2023towards"
] | {"problem_id":"dcb_lit_p2_003","task_type":"roa","name":"DynaCertBench System 024 · DCB-LIT-P2-003 · Example~3.1, \\cite{liu2023towards}","dynamics":"dx/dt = -x + x**3","equilibrium":[0],"stability_kind":"local_asymptotic","neighborhood":{"type":"constraint","lhs":"x**2","relation":"lt","rhs":"1","bounds":[[-1,1]]},"an... | {"record_id":"DCB-LIT-P2-003","problem":{"problem_id":"dcb_lit_p2_003","task_type":"roa","name":"DynaCertBench System 024 · DCB-LIT-P2-003 · Example~3.1, \\cite{liu2023towards}","dynamics":"dx/dt = -x + x**3","equilibrium":[0],"stability_kind":"local_asymptotic","neighborhood":{"type":"constraint","lhs":"x**2","relatio... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":2,"problem_name":"Region-of-attraction verification","raw_items_latex":["$x^\\star=0$","Original $\\mathcal{N}=(-1,1)$","Origi... |
DCB-LIT-P2-004 | 25 | roa | Region-of-attraction verification | literature | 2 | continuous | dx1/dt = x2, dx2/dt = -2*x1 + 1/3*x1**3 - x2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} x_2\\ -2x_1+\tfrac13x_1^3-x_2 \end{pmatrix}. \] | [
"liu2023towards"
] | {"problem_id":"dcb_lit_p2_004","task_type":"roa","name":"DynaCertBench System 025 · DCB-LIT-P2-004 · Example~6.2 and Table~II, \\cite{liu2023towards}","dynamics":"dx1/dt = x2, dx2/dt = -2*x1 + 1/3*x1**3 - x2","equilibrium":[0,0],"stability_kind":"local_asymptotic","neighborhood":{"type":"box","bounds":[[-6,6],[-6,6]]},... | {"record_id":"DCB-LIT-P2-004","problem":{"problem_id":"dcb_lit_p2_004","task_type":"roa","name":"DynaCertBench System 025 · DCB-LIT-P2-004 · Example~6.2 and Table~II, \\cite{liu2023towards}","dynamics":"dx1/dt = x2, dx2/dt = -2*x1 + 1/3*x1**3 - x2","equilibrium":[0,0],"stability_kind":"local_asymptotic","neighborhood":... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":2,"problem_name":"Region-of-attraction verification","raw_items_latex":["$x^\\star=(0,0)$","Original $\\mathcal{N}=[-6,6]^2$",... |
DCB-LIT-P2-005 | 26 | roa | Region-of-attraction verification | literature | 3 | continuous | dx1/dt = -10*(x1-x2) + u1, dx2/dt = 28*x1 - x2 - x1*x3 + u2, dx3/dt = x1*x2 - 8/3*x3 + u3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3 \end{pmatrix} = \begin{pmatrix} -10(x_1-x_2)+u_1\\ 28x_1-x_2-x_1x_3+u_2\\ x_1x_2-\dfrac83x_3+u_3 \end{pmatrix}. \] | [
"edwards2024fossil"
] | {"problem_id":"dcb_lit_p2_005","task_type":"roa","name":"DynaCertBench System 026 · DCB-LIT-P2-005 · Table~4 \\#3 (LorenzSystem), \\cite{edwards2024fossil}","dynamics":"dx1/dt = -10*(x1-x2) + u1, dx2/dt = 28*x1 - x2 - x1*x3 + u2, dx3/dt = x1*x2 - 8/3*x3 + u3","controller_parameters":"u1,u2,u3","equilibrium":[0,0,0],"st... | {"record_id":"DCB-LIT-P2-005","problem":{"problem_id":"dcb_lit_p2_005","task_type":"roa","name":"DynaCertBench System 026 · DCB-LIT-P2-005 · Table~4 \\#3 (LorenzSystem), \\cite{edwards2024fossil}","dynamics":"dx1/dt = -10*(x1-x2) + u1, dx2/dt = 28*x1 - x2 - x1*x3 + u2, dx3/dt = x1*x2 - 8/3*x3 + u3","controller_paramete... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","initial_set_X_I","neighborhood_N"],"set_contract_complete":true},"problem":2,"problem_name":"Region-of-attraction verification","raw_items_latex":["$x^\\star=(0,0,0)$","Original $\\ma... |
DCB-LIT-P2-006 | 27 | roa | Region-of-attraction verification | literature | 2 | continuous | dx1/dt = x2, dx2/dt = -1/2*x2-sin(x1+pi/3)+sin(pi/3) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} x_2\\ -0.5x_2-\sin\left(x_1+\dfrac{\pi}{3}\right) +\sin\left(\dfrac{\pi}{3}\right) \end{pmatrix}. \] | [
"liu2024tool"
] | {"problem_id":"dcb_lit_p2_006","task_type":"roa","name":"DynaCertBench System 027 · DCB-LIT-P2-006 · Example~5.2 and Table~2, \\cite{liu2024tool}","dynamics":"dx1/dt = x2, dx2/dt = -1/2*x2-sin(x1+pi/3)+sin(pi/3)","source":"paper System 27; canonical record DCB-LIT-P2-006","assumptions":["Transcribed from paper-4-20-202... | {"record_id":"DCB-LIT-P2-006","paper_system_number":27,"paper_system_label":"System 27","local_name":"S027__DCB-LIT-P2-006","problem":{"problem_id":"dcb_lit_p2_006","task_type":"roa","name":"DynaCertBench System 027 · DCB-LIT-P2-006 · Example~5.2 and Table~2, \\cite{liu2024tool}","dynamics":"dx1/dt = x2, dx2/dt = -1/2*... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":2,"problem_name":"Region-of-attraction verification","raw_items_latex":["$x^\\star=(0,0)$","Original $\\mathcal{N}=[-2,3]\\tim... |
DCB-LIT-P2-007 | 28 | roa | Region-of-attraction verification | literature | 10 | continuous | dx1/dt = -x1 + 1/2*x2 - 1/10*x9**2, dx2/dt = -1/2*x1 - x2, dx3/dt = -x3 + 1/2*x4 - 1/10*x1**2, dx4/dt = -1/2*x3 - x4, dx5/dt = -x5 + 1/2*x6 + 1/10*x7**2, dx6/dt = -1/2*x5 - x6, dx7/dt = -x7 + 1/2*x8, dx8/dt = -1/2*x7 - x8, dx9/dt = -x9 + 1/2*x10, dx10/dt = -1/2*x9 - x10 + 1/10*x2**2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4\\ \dot{x}_5\\ \dot{x}_6\\ \dot{x}_7\\ \dot{x}_8\\ \dot{x}_9\\ \dot{x}_{10} \end{pmatrix} = \begin{pmatrix} -x_1+0.5x_2-0.1x_9^2\\ -0.5x_1-x_2\\ -x_3+0.5x_4-0.1x_1^2\\ -0.5x_3-x_4\\ -x_5+0.5x_6+0.1x_7^2\\ -0.5x_... | [
"liu2024tool"
] | {"problem_id":"dcb_lit_p2_007","task_type":"roa","name":"DynaCertBench System 028 · DCB-LIT-P2-007 · Example~5.4 and Table~3, \\cite{liu2024tool}","dynamics":"dx1/dt = -x1 + 1/2*x2 - 1/10*x9**2, dx2/dt = -1/2*x1 - x2, dx3/dt = -x3 + 1/2*x4 - 1/10*x1**2, dx4/dt = -1/2*x3 - x4, dx5/dt = -x5 + 1/2*x6 + 1/10*x7**2, dx6/dt ... | {"record_id":"DCB-LIT-P2-007","problem":{"problem_id":"dcb_lit_p2_007","task_type":"roa","name":"DynaCertBench System 028 · DCB-LIT-P2-007 · Example~5.4 and Table~3, \\cite{liu2024tool}","dynamics":"dx1/dt = -x1 + 1/2*x2 - 1/10*x9**2, dx2/dt = -1/2*x1 - x2, dx3/dt = -x3 + 1/2*x4 - 1/10*x1**2, dx4/dt = -1/2*x3 - x4, dx5... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":2,"problem_name":"Region-of-attraction verification","raw_items_latex":["$x^\\star=\\mathbf{0}$","Original $\\mathcal{N}=[-1,1... |
DCB-LIT-P2-008 | 29 | roa | Region-of-attraction verification | literature | 1 | continuous | dx/dt = -x - x**3 | The closed-loop scalar dynamics are: \[ \dot{x}=-x-x^3, \] | [
"meng2024physics"
] | {"problem_id":"dcb_lit_p2_008","task_type":"roa","name":"DynaCertBench System 029 · DCB-LIT-P2-008 · Section~5.1, with verification details in Appendix~E.2 (\\(n=1\\)), \\cite{meng2024physics}","dynamics":"dx/dt = -x - x**3","equilibrium":[0],"stability_kind":"local_asymptotic","neighborhood":{"type":"box","bounds":[[-... | {"record_id":"DCB-LIT-P2-008","problem":{"problem_id":"dcb_lit_p2_008","task_type":"roa","name":"DynaCertBench System 029 · DCB-LIT-P2-008 · Section~5.1, with verification details in Appendix~E.2 (\\(n=1\\)), \\cite{meng2024physics}","dynamics":"dx/dt = -x - x**3","equilibrium":[0],"stability_kind":"local_asymptotic","... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":2,"problem_name":"Region-of-attraction verification","raw_items_latex":["Equilibrium: $x^\\star=0$","Original $ \\mathcal{N} =... |
DCB-LIT-P3-001 | 30 | invariant | Forward-invariant set synthesis | literature | 6 | discrete | x1[k+1] = x1+1/20*(x4*cos(x3)-x5*sin(x3)), x2[k+1] = x2+1/20*(x4*sin(x3)+x5*cos(x3)), x3[k+1] = x3+1/20*x6, x4[k+1] = x4+1/20*(x5*x6-49/5*sin(x3)), x5[k+1] = x5+1/20*(-x4*x6-49/5*cos(x3)+(u1+u2)/4), x6[k+1] = x6+1/20*((1/4)/(19/400)*(u1-u2)) | Let the state be ordered as \[ \mathbf{x} = (p_x,p_z,\phi,v_x,v_z,\omega)^\top \in \mathbb{R}^{6}, \] where $(p_x,p_z)$ are the planar position, $\phi$ is the roll angle, $(v_x,v_z)$ are the body-frame velocities, and $\omega$ is the angular rate. Using the sampling period $\Delta t=0.05$, the discrete-time transition ... | [
"wu2023neural"
] | {"problem_id":"dcb_lit_p3_001","task_type":"invariant","name":"DynaCertBench System 030 · DCB-LIT-P3-001 · Appendix~A.1 (PVTOL), \\cite{wu2023neural}","dynamics":"x1[k+1] = x1+1/20*(x4*cos(x3)-x5*sin(x3)), x2[k+1] = x2+1/20*(x4*sin(x3)+x5*cos(x3)), x3[k+1] = x3+1/20*x6, x4[k+1] = x4+1/20*(x5*x6-49/5*sin(x3)), x5[k+1] =... | {"record_id":"DCB-LIT-P3-001","problem":{"problem_id":"dcb_lit_p3_001","task_type":"invariant","name":"DynaCertBench System 030 · DCB-LIT-P3-001 · Appendix~A.1 (PVTOL), \\cite{wu2023neural}","dynamics":"x1[k+1] = x1+1/20*(x4*cos(x3)-x5*sin(x3)), x2[k+1] = x2+1/20*(x4*sin(x3)+x5*cos(x3)), x3[k+1] = x3+1/20*x6, x4[k+1] =... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","unsafe_set_X_U"],"set_contract_complete":true},"problem":3,"problem_name":"Forward-invariant set synthesis","raw_items_latex":["$ \\mathcal{X} = \\left\\{ \\mathbf{x}\\in\\mathbb{R}... |
DCB-LIT-P3-002 | 31 | invariant | Forward-invariant set synthesis | literature | 2 | continuous | dx1/dt = x2, dx2/dt = sin(x1)-3*x1-3*x2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} x_2\\[1ex] \sin(x_1) + u \end{pmatrix}, \] where $u = -3x_1 - 3x_2$. | [
"samanipour2026relu"
] | {"problem_id":"dcb_lit_p3_002","task_type":"invariant","name":"DynaCertBench System 031 · DCB-LIT-P3-002 · Example~1, \\cite{samanipour2026relu}","dynamics":"dx1/dt = x2, dx2/dt = sin(x1)-3*x1-3*x2","source":"paper System 31; canonical record DCB-LIT-P3-002","assumptions":["Deterministically normalized from canonical r... | {"record_id":"DCB-LIT-P3-002","problem":{"problem_id":"dcb_lit_p3_002","task_type":"invariant","name":"DynaCertBench System 031 · DCB-LIT-P3-002 · Example~1, \\cite{samanipour2026relu}","dynamics":"dx1/dt = x2, dx2/dt = sin(x1)-3*x1-3*x2","source":"paper System 31; canonical record DCB-LIT-P3-002","assumptions":["Deter... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","unsafe_set_X_U"],"set_contract_complete":true},"problem":3,"problem_name":"Forward-invariant set synthesis","raw_items_latex":["$\\mathcal{X} = \\{x\\in\\mathbb{R}^{2}\\mid \\lVert ... |
DCB-LIT-P3-003 | 32 | invariant | Forward-invariant set synthesis | literature | 2 | continuous | dx1/dt = x1**2+x1*x2+x1, dx2/dt = x1*x2+x2**2+x2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2} \end{pmatrix} = \begin{pmatrix} x_{1}^2 + x_{1}x_{2} + x_{1}\\[1ex] x_{1}x_{2} + x_{2}^2 + x_{2} \end{pmatrix}. \] | [
"samanipour2026relu"
] | {"problem_id":"dcb_lit_p3_003","task_type":"invariant","name":"DynaCertBench System 032 · DCB-LIT-P3-003 · Example~2, \\cite{samanipour2026relu}","dynamics":"dx1/dt = x1**2+x1*x2+x1, dx2/dt = x1*x2+x2**2+x2","source":"paper System 32; canonical record DCB-LIT-P3-003","assumptions":["Deterministically normalized from ca... | {"record_id":"DCB-LIT-P3-003","problem":{"problem_id":"dcb_lit_p3_003","task_type":"invariant","name":"DynaCertBench System 032 · DCB-LIT-P3-003 · Example~2, \\cite{samanipour2026relu}","dynamics":"dx1/dt = x1**2+x1*x2+x1, dx2/dt = x1*x2+x2**2+x2","source":"paper System 32; canonical record DCB-LIT-P3-003","assumptions... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","unsafe_set_X_U"],"set_contract_complete":true},"problem":3,"problem_name":"Forward-invariant set synthesis","raw_items_latex":["$\\mathcal{X} = \\{x\\in\\mathbb{R}^{2}\\mid \\lVert ... |
DCB-LIT-P3-004 | 33 | invariant | Forward-invariant set synthesis | literature | 4 | continuous | dx1/dt = x2, dx2/dt = ((x1+2.4109*x2+34.3620*x3+10.7009*x4)+(1/10)*x4**2*sin(x3)-(981/1000)*sin(x3)*cos(x3))/(1+(1/10)*sin(x3)**2), dx3/dt = x4, dx4/dt = ((10791/1000)*sin(x3)-(x1+2.4109*x2+34.3620*x3+10.7009*x4)*cos(x3)-(1/10)*x4**2*sin(x3)*cos(x3))/(1+(1/10)*sin(x3)**2) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4 \end{pmatrix} = \begin{pmatrix} x_2\\[1ex] \dfrac{u + 0.1\,x_4^2 \sin x_3 - 0.981 \sin x_3 \cos x_3}{1 + 0.1\sin^2 x_3}\\[2ex] x_4\\[1ex] \dfrac{10.791 \sin x_3 - u \cos x_3 - 0.1\,x_4^2 \sin x_3 \cos x_3}{1 + ... | [
"samanipour2026relu"
] | {"problem_id":"dcb_lit_p3_004","task_type":"invariant","name":"DynaCertBench System 033 · DCB-LIT-P3-004 · Example~3, \\cite{samanipour2026relu}","dynamics":"dx1/dt = x2, dx2/dt = ((x1+2.4109*x2+34.3620*x3+10.7009*x4)+(1/10)*x4**2*sin(x3)-(981/1000)*sin(x3)*cos(x3))/(1+(1/10)*sin(x3)**2), dx3/dt = x4, dx4/dt = ((10791/... | {"record_id":"DCB-LIT-P3-004","problem":{"problem_id":"dcb_lit_p3_004","task_type":"invariant","name":"DynaCertBench System 033 · DCB-LIT-P3-004 · Example~3, \\cite{samanipour2026relu}","dynamics":"dx1/dt = x2, dx2/dt = ((x1+2.4109*x2+34.3620*x3+10.7009*x4)+(1/10)*x4**2*sin(x3)-(981/1000)*sin(x3)*cos(x3))/(1+(1/10)*sin... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","unsafe_set_X_U"],"set_contract_complete":true},"problem":3,"problem_name":"Forward-invariant set synthesis","raw_items_latex":["$\\mathcal{X} = \\{x\\in\\mathbb{R}^{4}\\mid \\lVert ... |
DCB-LIT-P3-005 | 34 | invariant | Forward-invariant set synthesis | literature | 2 | discrete | x1[k+1] = x1+0.01*x2, x2[k+1] = x2+0.01*(9.8*sin(x1)+u) | The discrete-time transition map is: \[ \mathbf{x}^{+} = F(\mathbf{x}) = \begin{pmatrix} x_1 + 0.01\,x_2\\[1ex] x_2 + 0.01(9.8\sin x_1 + u) \end{pmatrix}, \] where $u \in [-10, 10]$. | [
"vaisi2025extracting"
] | {"problem_id":"dcb_lit_p3_005","task_type":"invariant","name":"DynaCertBench System 034 · DCB-LIT-P3-005 · Section~6.1.1, \\cite{vaisi2025extracting}","dynamics":"x1[k+1] = x1+0.01*x2, x2[k+1] = x2+0.01*(9.8*sin(x1)+u)","source":"paper System 34; canonical record DCB-LIT-P3-005","assumptions":["Deterministically normal... | {"record_id":"DCB-LIT-P3-005","problem":{"problem_id":"dcb_lit_p3_005","task_type":"invariant","name":"DynaCertBench System 034 · DCB-LIT-P3-005 · Section~6.1.1, \\cite{vaisi2025extracting}","dynamics":"x1[k+1] = x1+0.01*x2, x2[k+1] = x2+0.01*(9.8*sin(x1)+u)","source":"paper System 34; canonical record DCB-LIT-P3-005",... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","unsafe_set_X_U"],"set_contract_complete":true},"problem":3,"problem_name":"Forward-invariant set synthesis","raw_items_latex":["$\\mathcal{X} = \\{x\\in\\mathbb{R}^{2}\\mid \\lVert ... |
DCB-LIT-P3-006 | 35 | invariant | Forward-invariant set synthesis | literature | 3 | discrete | x1[k+1] = x2, x2[k+1] = 29.4*sin(x1)+300*cos(x1)*tan(x3)+15*u*cos(x1)*cos(x3)**2, x3[k+1] = u | The discrete-time transition map is: \[ \mathbf{x}^{+} = F(\mathbf{x}) = \begin{pmatrix} x_2\\[1ex] 29.4 \sin x_1 + 300 \cos x_1 \tan x_3 + 15 u \cos x_1 \cos^2 x_3\\[1ex] u \end{pmatrix}, \] where $u \in [-10, 10]$. | [
"vaisi2025extracting"
] | {"problem_id":"dcb_lit_p3_006","task_type":"invariant","name":"DynaCertBench System 035 · DCB-LIT-P3-006 · Section~6.1.2, \\cite{vaisi2025extracting}","dynamics":"x1[k+1] = x2, x2[k+1] = 29.4*sin(x1)+300*cos(x1)*tan(x3)+15*u*cos(x1)*cos(x3)**2, x3[k+1] = u","source":"paper System 35; canonical record DCB-LIT-P3-006","a... | {"record_id":"DCB-LIT-P3-006","problem":{"problem_id":"dcb_lit_p3_006","task_type":"invariant","name":"DynaCertBench System 035 · DCB-LIT-P3-006 · Section~6.1.2, \\cite{vaisi2025extracting}","dynamics":"x1[k+1] = x2, x2[k+1] = 29.4*sin(x1)+300*cos(x1)*tan(x3)+15*u*cos(x1)*cos(x3)**2, x3[k+1] = u","source":"paper System... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","unsafe_set_X_U"],"set_contract_complete":true},"problem":3,"problem_name":"Forward-invariant set synthesis","raw_items_latex":["$\\mathcal{X} = \\{x\\in\\mathbb{R}^{3}\\mid \\lVert ... |
DCB-LIT-P4-001 | 36 | safety | Safety verification | literature | 2 | continuous | dx1/dt = x2, dx2/dt = x1 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} x_2\\ x_1 \end{pmatrix}. \] | [
"sogokon2018vector"
] | {"problem_id":"dcb_lit_p4_001","task_type":"safety","name":"DynaCertBench System 036 · DCB-LIT-P4-001 · Theorem~4, \\cite{sogokon2018vector}","dynamics":"dx1/dt = x2, dx2/dt = x1","source":"paper System 36; canonical record DCB-LIT-P4-001","assumptions":["Deterministically normalized from canonical record DCB-LIT-P4-00... | {"record_id":"DCB-LIT-P4-001","problem":{"problem_id":"dcb_lit_p4_001","task_type":"safety","name":"DynaCertBench System 036 · DCB-LIT-P4-001 · Theorem~4, \\cite{sogokon2018vector}","dynamics":"dx1/dt = x2, dx2/dt = x1","source":"paper System 36; canonical record DCB-LIT-P4-001","assumptions":["Deterministically normal... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X}=\\mathbb{R}^{2}$","$\\mathcal{X}_... |
DCB-LIT-P4-002 | 37 | safety | Safety verification | literature | 3 | continuous | dx1/dt = 2*x1+x2+2*x3-x1**2+x1*x3-x3**2, dx2/dt = -2+x1-x2-x2**2, dx3/dt = -2-x2-x3+x1**2-x1*x3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3 \end{pmatrix} = \begin{pmatrix} 2x_1+x_2+2x_3-x_1^2+x_1x_3-x_3^2\\ -2+x_1-x_2-x_2^2\\ -2-x_2-x_3+x_1^2-x_1x_3 \end{pmatrix}. \] | [
"sogokon2018vector"
] | {"problem_id":"dcb_lit_p4_002","task_type":"safety","name":"DynaCertBench System 037 · DCB-LIT-P4-002 · Example~1, \\cite{sogokon2018vector}","dynamics":"dx1/dt = 2*x1+x2+2*x3-x1**2+x1*x3-x3**2, dx2/dt = -2+x1-x2-x2**2, dx3/dt = -2-x2-x3+x1**2-x1*x3","source":"paper System 37; canonical record DCB-LIT-P4-002","assumpti... | {"record_id":"DCB-LIT-P4-002","problem":{"problem_id":"dcb_lit_p4_002","task_type":"safety","name":"DynaCertBench System 037 · DCB-LIT-P4-002 · Example~1, \\cite{sogokon2018vector}","dynamics":"dx1/dt = 2*x1+x2+2*x3-x1**2+x1*x3-x3**2, dx2/dt = -2+x1-x2-x2**2, dx3/dt = -2-x2-x3+x1**2-x1*x3","source":"paper System 37; ca... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X}=\\mathbb{R}^{3}$","$\\mathcal{X}_... |
DCB-LIT-P4-003 | 38 | safety | Safety verification | literature | 2 | continuous | dx1/dt = x2, dx2/dt = -x1+((1)/(3))*x1**3-x2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} x_2\\ -x_1+\tfrac13x_1^3-x_2 \end{pmatrix}. \] | [
"zhao2020synthesizing"
] | {"problem_id":"dcb_lit_p4_003","task_type":"safety","name":"DynaCertBench System 038 · DCB-LIT-P4-003 · Example~3.1, \\cite{zhao2020synthesizing}","dynamics":"dx1/dt = x2, dx2/dt = -x1+((1)/(3))*x1**3-x2","source":"paper System 38; canonical record DCB-LIT-P4-003","assumptions":["Deterministically normalized from canon... | {"record_id":"DCB-LIT-P4-003","problem":{"problem_id":"dcb_lit_p4_003","task_type":"safety","name":"DynaCertBench System 038 · DCB-LIT-P4-003 · Example~3.1, \\cite{zhao2020synthesizing}","dynamics":"dx1/dt = x2, dx2/dt = -x1+((1)/(3))*x1**3-x2","source":"paper System 38; canonical record DCB-LIT-P4-003","assumptions":[... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X}= \\{\\mathbf{x}\\in\\mathbb{R}^{2... |
DCB-LIT-P4-004 | 39 | safety | Safety verification | literature | 2 | continuous | dx1/dt = x2+2*x1*x2, dx2/dt = -x1-x2**2+2*x1**2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} x_2+2x_1x_2\\ -x_1-x_2^2+2x_1^2 \end{pmatrix}. \] | [
"abate2021fossil"
] | {"problem_id":"dcb_lit_p4_004","task_type":"safety","name":"DynaCertBench System 039 · DCB-LIT-P4-004 · Table~1 row~9 (Barr1), \\cite{abate2021fossil}","dynamics":"dx1/dt = x2+2*x1*x2, dx2/dt = -x1-x2**2+2*x1**2","source":"paper System 39; canonical record DCB-LIT-P4-004","assumptions":["Deterministically normalized fr... | {"record_id":"DCB-LIT-P4-004","problem":{"problem_id":"dcb_lit_p4_004","task_type":"safety","name":"DynaCertBench System 039 · DCB-LIT-P4-004 · Table~1 row~9 (Barr1), \\cite{abate2021fossil}","dynamics":"dx1/dt = x2+2*x1*x2, dx2/dt = -x1-x2**2+2*x1**2","source":"paper System 39; canonical record DCB-LIT-P4-004","assump... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X}=[-2,2]^2$","$\\mathcal{X}_I=[0,1]... |
DCB-LIT-P4-005 | 40 | safety | Safety verification | literature | 3 | continuous | dx1/dt = sin(x3), dx2/dt = cos(x3), dx3/dt = -sin(x3)+((3*(x1*sin(x3)+x2*cos(x3)))/(0.5+x1**2+x2**2)) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{\phi} \end{pmatrix} = \begin{pmatrix} \sin(\phi)\\ \cos(\phi)\\ -\sin(\phi)+ \dfrac{3(x_1\sin(\phi)+x_2\cos(\phi))} {0.5+x_1^2+x_2^2} \end{pmatrix}. \] | [
"abate2021fossil"
] | {"problem_id":"dcb_lit_p4_005","task_type":"safety","name":"DynaCertBench System 040 · DCB-LIT-P4-005 · Table~1 row~12 (Barr4), \\cite{abate2021fossil}","dynamics":"dx1/dt = sin(x3), dx2/dt = cos(x3), dx3/dt = -sin(x3)+((3*(x1*sin(x3)+x2*cos(x3)))/(0.5+x1**2+x2**2))","source":"paper System 40; canonical record DCB-LIT-... | {"record_id":"DCB-LIT-P4-005","problem":{"problem_id":"dcb_lit_p4_005","task_type":"safety","name":"DynaCertBench System 040 · DCB-LIT-P4-005 · Table~1 row~12 (Barr4), \\cite{abate2021fossil}","dynamics":"dx1/dt = sin(x3), dx2/dt = cos(x3), dx3/dt = -sin(x3)+((3*(x1*sin(x3)+x2*cos(x3)))/(0.5+x1**2+x2**2))","source":"pa... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X}=[-2,2]\\times[-2,2]\\times[-1.57,... |
DCB-LIT-P4-006 | 41 | safety | Safety verification | literature | 8 | continuous | dx0/dt = x1, dx1/dt = x2, dx2/dt = x3, dx3/dt = x4, dx4/dt = x5, dx5/dt = x6, dx6/dt = x7, dx7/dt = -(20*x7 + 170*x6 + 800*x5 + 2273*x4 + 3980*x3 + 4180*x2 + 2400*x1 + 576*x0) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_0\\ \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4\\ \dot{x}_5\\ \dot{x}_6\\ \dot{x}_7 \end{pmatrix} = \begin{pmatrix} x_1\\ x_2\\ x_3\\ x_4\\ x_5\\ x_6\\ x_7\\ -\begin{aligned}[t] &20x_7+170x_6+800x_5+2273x_4\\[-0.15ex] &{}+3980x_3+4180x_2+2400x_1+... | [
"abate2021fossil"
] | {"problem_id":"dcb_lit_p4_006","task_type":"safety","name":"DynaCertBench System 041 · DCB-LIT-P4-006 · Table~1 row~17 (Hi-Ord8), \\cite{abate2021fossil}","dynamics":"dx0/dt = x1, dx1/dt = x2, dx2/dt = x3, dx3/dt = x4, dx4/dt = x5, dx5/dt = x6, dx6/dt = x7, dx7/dt = -(20*x7 + 170*x6 + 800*x5 + 2273*x4 + 3980*x3 + 4180*... | {"record_id":"DCB-LIT-P4-006","problem":{"problem_id":"dcb_lit_p4_006","task_type":"safety","name":"DynaCertBench System 041 · DCB-LIT-P4-006 · Table~1 row~17 (Hi-Ord8), \\cite{abate2021fossil}","dynamics":"dx0/dt = x1, dx1/dt = x2, dx2/dt = x3, dx3/dt = x4, dx4/dt = x5, dx5/dt = x6, dx6/dt = x7, dx7/dt = -(20*x7 + 170... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X}=[-2.2,2.2]^8$","$\\mathcal{X}_I=[... |
DCB-LIT-P4-007 | 42 | safety | Safety verification | literature | 2 | continuous | dx1/dt = x1**2+x2**2-1, dx2/dt = 5*(x1*x2-1) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} x_1^2+x_2^2-1\\ 5(x_1x_2-1) \end{pmatrix}. \] | [
"wu2024completeness"
] | {"problem_id":"dcb_lit_p4_007","task_type":"safety","name":"DynaCertBench System 042 · DCB-LIT-P4-007 · Table~1 (arch2[36], instance~1), \\cite{wu2024completeness}","dynamics":"dx1/dt = x1**2+x2**2-1, dx2/dt = 5*(x1*x2-1)","source":"paper System 42; canonical record DCB-LIT-P4-007","assumptions":["Deterministically nor... | {"record_id":"DCB-LIT-P4-007","problem":{"problem_id":"dcb_lit_p4_007","task_type":"safety","name":"DynaCertBench System 042 · DCB-LIT-P4-007 · Table~1 (arch2[36], instance~1), \\cite{wu2024completeness}","dynamics":"dx1/dt = x1**2+x2**2-1, dx2/dt = 5*(x1*x2-1)","source":"paper System 42; canonical record DCB-LIT-P4-00... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X}=\\mathbb{R}^{2}$","$\\mathcal{X}_... |
DCB-LIT-P4-008 | 43 | safety | Safety verification | literature | 2 | continuous | dx1/dt = x1-x1**3+x2-x1*x2**2, dx2/dt = -x1+x2-x1**2*x2-x2**3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} x_1-x_1^3+x_2-x_1x_2^2\\ -x_1+x_2-x_1^2x_2-x_2^3 \end{pmatrix}. \] | [
"wu2024completeness"
] | {"problem_id":"dcb_lit_p4_008","task_type":"safety","name":"DynaCertBench System 043 · DCB-LIT-P4-008 · Table~1 (arch3[36], instance~1), \\cite{wu2024completeness}","dynamics":"dx1/dt = x1-x1**3+x2-x1*x2**2, dx2/dt = -x1+x2-x1**2*x2-x2**3","source":"paper System 43; canonical record DCB-LIT-P4-008","assumptions":["Dete... | {"record_id":"DCB-LIT-P4-008","problem":{"problem_id":"dcb_lit_p4_008","task_type":"safety","name":"DynaCertBench System 043 · DCB-LIT-P4-008 · Table~1 (arch3[36], instance~1), \\cite{wu2024completeness}","dynamics":"dx1/dt = x1-x1**3+x2-x1*x2**2, dx2/dt = -x1+x2-x1**2*x2-x2**3","source":"paper System 43; canonical rec... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X}=\\mathbb{R}^{2}$","$\\mathcal{X}_... |
DCB-LIT-P4-009 | 44 | safety | Safety verification | literature | 2 | continuous | dx1/dt = exp(-x1)+x2-1, dx2/dt = -sin(x1)**2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} e^{-x_1}+x_2-1\\ -\sin^2(x_1) \end{pmatrix}. \] | [
"liu2015abstraction"
] | {"problem_id":"dcb_lit_p4_009","task_type":"safety","name":"DynaCertBench System 044 · DCB-LIT-P4-009 · Example~5 and Table~1, \\cite{liu2015abstraction}","dynamics":"dx1/dt = exp(-x1)+x2-1, dx2/dt = -sin(x1)**2","source":"paper System 44; canonical record DCB-LIT-P4-009","assumptions":["Deterministically normalized fr... | {"record_id":"DCB-LIT-P4-009","problem":{"problem_id":"dcb_lit_p4_009","task_type":"safety","name":"DynaCertBench System 044 · DCB-LIT-P4-009 · Example~5 and Table~1, \\cite{liu2015abstraction}","dynamics":"dx1/dt = exp(-x1)+x2-1, dx2/dt = -sin(x1)**2","source":"paper System 44; canonical record DCB-LIT-P4-009","assump... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X}=[-2,2]^2$","$\\mathcal{X}_I= \\{(... |
DCB-LIT-P4-010 | 45 | safety | Safety verification | literature | 3 | continuous | dx1/dt = -(((1/5)*10*x1*x2)/(x1+x2+x3))-(1/125)*x1, dx2/dt = (((1/5)*10*x1*x2)/(x1+x2+x3))-((1/125)+(1/10))*x2, dx3/dt = 1/10*x2-19/20*x3 | The vector flow field is: \[ \dot{\mathbf{u}} = \begin{pmatrix} \dot{u}_1\\ \dot{u}_2\\ \dot{u}_3 \end{pmatrix} = \begin{pmatrix} -\dfrac{\beta c u_1u_2}{u_1+u_2+u_3}-\mu u_1\\ \dfrac{\beta c u_1u_2}{u_1+u_2+u_3}-(\mu+\nu)u_2\\ \nu u_2-\alpha u_3 \end{pmatrix}, \] where $\beta=0.2$, $c=10$, $\mu=0.008$, $\alpha=0.95$, ... | [
"liu2015abstraction"
] | {"problem_id":"dcb_lit_p4_010","task_type":"safety","name":"DynaCertBench System 045 · DCB-LIT-P4-010 · Example~6 and Table~1, \\cite{liu2015abstraction}","dynamics":"dx1/dt = -(((1/5)*10*x1*x2)/(x1+x2+x3))-(1/125)*x1, dx2/dt = (((1/5)*10*x1*x2)/(x1+x2+x3))-((1/125)+(1/10))*x2, dx3/dt = 1/10*x2-19/20*x3","source":"pape... | {"record_id":"DCB-LIT-P4-010","problem":{"problem_id":"dcb_lit_p4_010","task_type":"safety","name":"DynaCertBench System 045 · DCB-LIT-P4-010 · Example~6 and Table~1, \\cite{liu2015abstraction}","dynamics":"dx1/dt = -(((1/5)*10*x1*x2)/(x1+x2+x3))-(1/125)*x1, dx2/dt = (((1/5)*10*x1*x2)/(x1+x2+x3))-((1/125)+(1/10))*x2, d... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X}=\\{\\mathbf{u}\\in\\mathbb{R}^{3}... |
DCB-LIT-P4-011 | 46 | safety | Safety verification | literature | 3 | continuous | dx1/dt = x1*(1-x3), dx2/dt = x2*(1-2*x3), dx3/dt = x3*(x1+x2-1) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3 \end{pmatrix} = \begin{pmatrix} x_1(1-x_3)\\ x_2(1-2x_3)\\ x_3(x_1+x_2-1) \end{pmatrix}. \] | [
"wu2024completeness"
] | {"problem_id":"dcb_lit_p4_011","task_type":"safety","name":"DynaCertBench System 046 · DCB-LIT-P4-011 · Table~1 (lotka[14], instance~1), \\cite{wu2024completeness}","dynamics":"dx1/dt = x1*(1-x3), dx2/dt = x2*(1-2*x3), dx3/dt = x3*(x1+x2-1)","source":"paper System 46; canonical record DCB-LIT-P4-011","assumptions":["De... | {"record_id":"DCB-LIT-P4-011","problem":{"problem_id":"dcb_lit_p4_011","task_type":"safety","name":"DynaCertBench System 046 · DCB-LIT-P4-011 · Table~1 (lotka[14], instance~1), \\cite{wu2024completeness}","dynamics":"dx1/dt = x1*(1-x3), dx2/dt = x2*(1-2*x3), dx3/dt = x3*(x1+x2-1)","source":"paper System 46; canonical r... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X}=\\mathbb{R}^{3}$","$\\mathcal{X}_... |
DCB-LIT-P4-012 | 47 | safety | Safety verification | literature | 3 | continuous | dx1/dt = sin(x3), dx2/dt = cos(x3), dx3/dt = -sin(x3)+u1 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{\phi} \end{pmatrix} = \begin{pmatrix} \sin(\phi)\\ \cos(\phi)\\ -\sin(\phi)+u_1 \end{pmatrix}. \] | [
"edwards2024fossil"
] | {"problem_id":"dcb_lit_p4_012","task_type":"safety","name":"DynaCertBench System 047 · DCB-LIT-P4-012 · Table~4 \\#5 (ctrlbarr obstacle), \\cite{edwards2024fossil}","dynamics":"dx1/dt = sin(x3), dx2/dt = cos(x3), dx3/dt = -sin(x3)+u1","source":"paper System 47; canonical record DCB-LIT-P4-012","assumptions":["Determini... | {"record_id":"DCB-LIT-P4-012","problem":{"problem_id":"dcb_lit_p4_012","task_type":"safety","name":"DynaCertBench System 047 · DCB-LIT-P4-012 · Table~4 \\#5 (ctrlbarr obstacle), \\cite{edwards2024fossil}","dynamics":"dx1/dt = sin(x3), dx2/dt = cos(x3), dx3/dt = -sin(x3)+u1","source":"paper System 47; canonical record D... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X}=[-10,10]\\times[-10,10]\\times[-\... |
DCB-LIT-P4-013 | 48 | safety | Safety verification | literature | 2 | discrete | x1[k+1] = 0.725*x1+0.25*x2+0.375+0.018*(55-x1)*u1, x2[k+1] = 0.25*x1+0.71*x2+0.6+0.018*(55-x2)*u2 | The discrete-time transition map is: \[ \mathbf{x}^{+} = F(\mathbf{x},\mathbf{u}) = \begin{pmatrix} 0.725x_1+0.25x_2+0.375+0.018(55-x_1)u_1\\ 0.25x_1+0.71x_2+0.6+0.018(55-x_2)u_2 \end{pmatrix}. \] | [
"edwards2024fossil"
] | {"problem_id":"dcb_lit_p4_013","task_type":"safety","name":"DynaCertBench System 048 · DCB-LIT-P4-013 · Table~4 \\#17 (ctrlbarr 2roomtemp DT), \\cite{edwards2024fossil}","dynamics":"x1[k+1] = 0.725*x1+0.25*x2+0.375+0.018*(55-x1)*u1, x2[k+1] = 0.25*x1+0.71*x2+0.6+0.018*(55-x2)*u2","source":"paper System 48; canonical re... | {"record_id":"DCB-LIT-P4-013","problem":{"problem_id":"dcb_lit_p4_013","task_type":"safety","name":"DynaCertBench System 048 · DCB-LIT-P4-013 · Table~4 \\#17 (ctrlbarr 2roomtemp DT), \\cite{edwards2024fossil}","dynamics":"x1[k+1] = 0.725*x1+0.25*x2+0.375+0.018*(55-x1)*u1, x2[k+1] = 0.25*x1+0.71*x2+0.6+0.018*(55-x2)*u2"... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X}=[17,30]^2$","$\\mathcal{X}_I=[17,... |
DCB-LIT-P4-014 | 49 | safety | Safety verification | literature | 3 | continuous | dx1/dt = x2+u0, dx2/dt = -0.8*x1-0.15*x2+0.2*x1**(2)+u1, dx3/dt = -0.1*x3+0.1*x1+u2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3} \end{pmatrix} = \begin{pmatrix} x_{2} + u_{0}\\ -0.8\,x_{1} - 0.15\,x_{2} + 0.2\,x_{1}^{2} + u_{1}\\ -0.1\,x_{3} + 0.1\,x_{1} + u_{2} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_014","task_type":"safety","name":"DynaCertBench System 049 · DCB-LIT-P4-014 · ~\\texttt{S001}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.8*x1-0.15*x2+0.2*x1**(2)+u1, dx3/dt = -0.1*x3+0.1*x1+u2","source":"paper System 49; canonical record DCB-LIT-P4-014","assumptio... | {"record_id":"DCB-LIT-P4-014","problem":{"problem_id":"dcb_lit_p4_014","task_type":"safety","name":"DynaCertBench System 049 · DCB-LIT-P4-014 · ~\\texttt{S001}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.8*x1-0.15*x2+0.2*x1**(2)+u1, dx3/dt = -0.1*x3+0.1*x1+u2","source":"paper System 49; can... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-015 | 50 | safety | Safety verification | literature | 4 | continuous | dx1/dt = x2+u0, dx2/dt = -0.95*sin(x1)-0.02*x2+0.01*x3+u1, dx3/dt = -0.1*x3+0.02*x1+u2, dx4/dt = -0.03*x4+0.01*x2+u3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3}\\ \dot{x}_{4} \end{pmatrix} = \begin{pmatrix} x_{2} + u_{0}\\ -0.95\,\sin(x_{1}) - 0.02\,x_{2} + 0.01\,x_{3} + u_{1}\\ -0.1\,x_{3} + 0.02\,x_{1} + u_{2}\\ -0.03\,x_{4} + 0.01\,x_{2} + u_{3} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_015","task_type":"safety","name":"DynaCertBench System 050 · DCB-LIT-P4-015 · ~\\texttt{S002}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.95*sin(x1)-0.02*x2+0.01*x3+u1, dx3/dt = -0.1*x3+0.02*x1+u2, dx4/dt = -0.03*x4+0.01*x2+u3","source":"paper System 50; canonical ... | {"record_id":"DCB-LIT-P4-015","problem":{"problem_id":"dcb_lit_p4_015","task_type":"safety","name":"DynaCertBench System 050 · DCB-LIT-P4-015 · ~\\texttt{S002}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.95*sin(x1)-0.02*x2+0.01*x3+u1, dx3/dt = -0.1*x3+0.02*x1+u2, dx4/dt = -0.03*x4+0.01*x2+u... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{4}$","$\\mathcal{X... |
DCB-LIT-P4-016 | 51 | safety | Safety verification | literature | 4 | continuous | dx1/dt = 10*(x2-x1)+u0, dx2/dt = 28*x1-x2-x1*x3+u1, dx3/dt = x1*x2-((8)/(3))*x3+u2, dx4/dt = -x2*x3+2.7*x4+u3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3}\\ \dot{x}_{4} \end{pmatrix} = \begin{pmatrix} 10\,(x_{2} - x_{1}) + u_{0}\\ 28\,x_{1} - x_{2} - x_{1}\,x_{3} + u_{1}\\ x_{1}\,x_{2} - \frac{8}{3}\,x_{3} + u_{2}\\ -x_{2}\,x_{3} + 2.7\,x_{4} + u_{3} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_016","task_type":"safety","name":"DynaCertBench System 051 · DCB-LIT-P4-016 · ~\\texttt{S004}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = 10*(x2-x1)+u0, dx2/dt = 28*x1-x2-x1*x3+u1, dx3/dt = x1*x2-((8)/(3))*x3+u2, dx4/dt = -x2*x3+2.7*x4+u3","source":"paper System 51; canonical record ... | {"record_id":"DCB-LIT-P4-016","problem":{"problem_id":"dcb_lit_p4_016","task_type":"safety","name":"DynaCertBench System 051 · DCB-LIT-P4-016 · ~\\texttt{S004}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = 10*(x2-x1)+u0, dx2/dt = 28*x1-x2-x1*x3+u1, dx3/dt = x1*x2-((8)/(3))*x3+u2, dx4/dt = -x2*x3+2.7*x4+u3","sou... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{4}$","$\\mathcal{X... |
DCB-LIT-P4-017 | 52 | safety | Safety verification | literature | 3 | continuous | dx1/dt = -2*x1+6.7*x2-x2*x3+u0, dx2/dt = x1+u1, dx3/dt = -x3+x2**(2)+u2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3} \end{pmatrix} = \begin{pmatrix} -2\,x_{1} + 6.7\,x_{2} - x_{2}\,x_{3} + u_{0}\\ x_{1} + u_{1}\\ -x_{3} + x_{2}^{2} + u_{2} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_017","task_type":"safety","name":"DynaCertBench System 052 · DCB-LIT-P4-017 · ~\\texttt{S008}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -2*x1+6.7*x2-x2*x3+u0, dx2/dt = x1+u1, dx3/dt = -x3+x2**(2)+u2","source":"paper System 52; canonical record DCB-LIT-P4-017","assumptions":["Determ... | {"record_id":"DCB-LIT-P4-017","problem":{"problem_id":"dcb_lit_p4_017","task_type":"safety","name":"DynaCertBench System 052 · DCB-LIT-P4-017 · ~\\texttt{S008}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -2*x1+6.7*x2-x2*x3+u0, dx2/dt = x1+u1, dx3/dt = -x3+x2**(2)+u2","source":"paper System 52; canonical recor... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-018 | 53 | safety | Safety verification | literature | 2 | continuous | dx1/dt = x2+u0, dx2/dt = -0.3*x1-0.2*(1+cos(x1))*x2-0.1*x1**(3)+u1 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2} \end{pmatrix} = \begin{pmatrix} x_{2} + u_{0}\\ -0.3\,x_{1} - 0.2\,(1 + \cos(x_{1}))\,x_{2} - 0.1\,x_{1}^{3} + u_{1} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_018","task_type":"safety","name":"DynaCertBench System 053 · DCB-LIT-P4-018 · ~\\texttt{S011}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.3*x1-0.2*(1+cos(x1))*x2-0.1*x1**(3)+u1","source":"paper System 53; canonical record DCB-LIT-P4-018","assumptions":["Determinist... | {"record_id":"DCB-LIT-P4-018","problem":{"problem_id":"dcb_lit_p4_018","task_type":"safety","name":"DynaCertBench System 053 · DCB-LIT-P4-018 · ~\\texttt{S011}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.3*x1-0.2*(1+cos(x1))*x2-0.1*x1**(3)+u1","source":"paper System 53; canonical record DCB... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{2}$","$\\mathcal{X... |
DCB-LIT-P4-019 | 54 | safety | Safety verification | literature | 3 | continuous | dx1/dt = -x1+x2*x3, dx2/dt = -x2+x1*x3, dx3/dt = -x3-x1*x2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3} \end{pmatrix} = \begin{pmatrix} -x_{1} + x_{2}\,x_{3}\\ -x_{2} + x_{1}\,x_{3}\\ -x_{3} - x_{1}\,x_{2} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_019","task_type":"safety","name":"DynaCertBench System 054 · DCB-LIT-P4-019 · ~\\texttt{S019}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -x1+x2*x3, dx2/dt = -x2+x1*x3, dx3/dt = -x3-x1*x2","source":"paper System 54; canonical record DCB-LIT-P4-019","assumptions":["Deterministically n... | {"record_id":"DCB-LIT-P4-019","problem":{"problem_id":"dcb_lit_p4_019","task_type":"safety","name":"DynaCertBench System 054 · DCB-LIT-P4-019 · ~\\texttt{S019}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -x1+x2*x3, dx2/dt = -x2+x1*x3, dx3/dt = -x3-x1*x2","source":"paper System 54; canonical record DCB-LIT-P4-... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-020 | 55 | safety | Safety verification | literature | 4 | continuous | dx1/dt = x2+u0, dx2/dt = -x1-0.4*x2+0.15*sin(x3)+u1, dx3/dt = x4+u2, dx4/dt = -0.6*x3-0.3*x4+u3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3}\\ \dot{x}_{4} \end{pmatrix} = \begin{pmatrix} x_{2} + u_{0}\\ -x_{1} - 0.4\,x_{2} + 0.15\,\sin(x_{3}) + u_{1}\\ x_{4} + u_{2}\\ -0.6\,x_{3} - 0.3\,x_{4} + u_{3} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_020","task_type":"safety","name":"DynaCertBench System 055 · DCB-LIT-P4-020 · ~\\texttt{S024}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -x1-0.4*x2+0.15*sin(x3)+u1, dx3/dt = x4+u2, dx4/dt = -0.6*x3-0.3*x4+u3","source":"paper System 55; canonical record DCB-LIT-P4-020... | {"record_id":"DCB-LIT-P4-020","problem":{"problem_id":"dcb_lit_p4_020","task_type":"safety","name":"DynaCertBench System 055 · DCB-LIT-P4-020 · ~\\texttt{S024}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -x1-0.4*x2+0.15*sin(x3)+u1, dx3/dt = x4+u2, dx4/dt = -0.6*x3-0.3*x4+u3","source":"paper Sy... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{4}$","$\\mathcal{X... |
DCB-LIT-P4-021 | 56 | safety | Safety verification | literature | 3 | continuous | dx1/dt = -0.4*x1+0.25*x2*x3-0.15*x1**(3), dx2/dt = -0.5*x2+0.3*x1*x3-0.2*x2**(3), dx3/dt = -0.6*x3+0.2*x1*x2-0.18*x1**(2)*x2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3} \end{pmatrix} = \begin{pmatrix} -0.4\,x_{1} + 0.25\,x_{2}\,x_{3} - 0.15\,x_{1}^{3}\\ -0.5\,x_{2} + 0.3\,x_{1}\,x_{3} - 0.2\,x_{2}^{3}\\ -0.6\,x_{3} + 0.2\,x_{1}\,x_{2} - 0.18\,x_{1}^{2}\,x_{2} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_021","task_type":"safety","name":"DynaCertBench System 056 · DCB-LIT-P4-021 · ~\\texttt{S028}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.4*x1+0.25*x2*x3-0.15*x1**(3), dx2/dt = -0.5*x2+0.3*x1*x3-0.2*x2**(3), dx3/dt = -0.6*x3+0.2*x1*x2-0.18*x1**(2)*x2","source":"paper System 56; ca... | {"record_id":"DCB-LIT-P4-021","problem":{"problem_id":"dcb_lit_p4_021","task_type":"safety","name":"DynaCertBench System 056 · DCB-LIT-P4-021 · ~\\texttt{S028}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.4*x1+0.25*x2*x3-0.15*x1**(3), dx2/dt = -0.5*x2+0.3*x1*x3-0.2*x2**(3), dx3/dt = -0.6*x3+0.2*x1*x2-0.18*x... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-022 | 57 | safety | Safety verification | literature | 4 | continuous | dx1/dt = -0.3*x1+0.2*x2*x4-0.15*x3**(2), dx2/dt = -0.4*x2+0.25*x1*x3-0.18*x2*x4, dx3/dt = -0.5*x3+0.3*x1*x4+0.12*x2**(2), dx4/dt = -0.6*x4+0.2*x2*x3-0.1*x1**(2)*x4 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3}\\ \dot{x}_{4} \end{pmatrix} = \begin{pmatrix} -0.3\,x_{1} + 0.2\,x_{2}\,x_{4} - 0.15\,x_{3}^{2}\\ -0.4\,x_{2} + 0.25\,x_{1}\,x_{3} - 0.18\,x_{2}\,x_{4}\\ -0.5\,x_{3} + 0.3\,x_{1}\,x_{4} + 0.12\,x_{2}^{2}\\ -0.6\,x_{4... | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_022","task_type":"safety","name":"DynaCertBench System 057 · DCB-LIT-P4-022 · ~\\texttt{S031}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.3*x1+0.2*x2*x4-0.15*x3**(2), dx2/dt = -0.4*x2+0.25*x1*x3-0.18*x2*x4, dx3/dt = -0.5*x3+0.3*x1*x4+0.12*x2**(2), dx4/dt = -0.6*x4+0.2*x2*x3-0.1*x1... | {"record_id":"DCB-LIT-P4-022","problem":{"problem_id":"dcb_lit_p4_022","task_type":"safety","name":"DynaCertBench System 057 · DCB-LIT-P4-022 · ~\\texttt{S031}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.3*x1+0.2*x2*x4-0.15*x3**(2), dx2/dt = -0.4*x2+0.25*x1*x3-0.18*x2*x4, dx3/dt = -0.5*x3+0.3*x1*x4+0.12*x2... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{4}$","$\\mathcal{X... |
DCB-LIT-P4-023 | 58 | safety | Safety verification | literature | 2 | discrete | x1[k+1] = 0.85*x1[k]+u0[k], x2[k+1] = 0.8*x2[k]+0.15*x1[k]+u1[k] | The update map is: \[ \mathbf{x}_{k+1} = \begin{pmatrix} x_{1,k+1}\\ x_{2,k+1} \end{pmatrix} = \begin{pmatrix} 0.85\,x_{1,k} + u_{0,k}\\ 0.8\,x_{2,k} + 0.15\,x_{1,k} + u_{1,k} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_023","task_type":"safety","name":"DynaCertBench System 058 · DCB-LIT-P4-023 · ~\\texttt{S036}, \\cite{taheri2025barrierbench}","dynamics":"x1[k+1] = 0.85*x1[k]+u0[k], x2[k+1] = 0.8*x2[k]+0.15*x1[k]+u1[k]","source":"paper System 58; canonical record DCB-LIT-P4-023","assumptions":["Deterministic... | {"record_id":"DCB-LIT-P4-023","problem":{"problem_id":"dcb_lit_p4_023","task_type":"safety","name":"DynaCertBench System 058 · DCB-LIT-P4-023 · ~\\texttt{S036}, \\cite{taheri2025barrierbench}","dynamics":"x1[k+1] = 0.85*x1[k]+u0[k], x2[k+1] = 0.8*x2[k]+0.15*x1[k]+u1[k]","source":"paper System 58; canonical record DCB-L... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{2}$","$\\mathcal{X... |
DCB-LIT-P4-024 | 59 | safety | Safety verification | literature | 2 | continuous | dx1/dt = x2+u0, dx2/dt = -0.2*x1-0.1*(x1**(2)-1)*x2+u1 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2} \end{pmatrix} = \begin{pmatrix} x_{2} + u_{0}\\ -0.2\,x_{1} - 0.1\,(x_{1}^{2} - 1)\,x_{2} + u_{1} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_024","task_type":"safety","name":"DynaCertBench System 059 · DCB-LIT-P4-024 · ~\\texttt{S037}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.2*x1-0.1*(x1**(2)-1)*x2+u1","source":"paper System 59; canonical record DCB-LIT-P4-024","assumptions":["Deterministically norma... | {"record_id":"DCB-LIT-P4-024","problem":{"problem_id":"dcb_lit_p4_024","task_type":"safety","name":"DynaCertBench System 059 · DCB-LIT-P4-024 · ~\\texttt{S037}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.2*x1-0.1*(x1**(2)-1)*x2+u1","source":"paper System 59; canonical record DCB-LIT-P4-024"... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{2}$","$\\mathcal{X... |
DCB-LIT-P4-025 | 60 | safety | Safety verification | literature | 4 | continuous | dx1/dt = x2+u0, dx2/dt = -0.6*x1-0.1*x2+0.05*x3+u1, dx3/dt = x4+u2, dx4/dt = -0.8*x3-0.15*x4+0.05*x1+u3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3}\\ \dot{x}_{4} \end{pmatrix} = \begin{pmatrix} x_{2} + u_{0}\\ -0.6\,x_{1} - 0.1\,x_{2} + 0.05\,x_{3} + u_{1}\\ x_{4} + u_{2}\\ -0.8\,x_{3} - 0.15\,x_{4} + 0.05\,x_{1} + u_{3} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_025","task_type":"safety","name":"DynaCertBench System 060 · DCB-LIT-P4-025 · ~\\texttt{S042}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.6*x1-0.1*x2+0.05*x3+u1, dx3/dt = x4+u2, dx4/dt = -0.8*x3-0.15*x4+0.05*x1+u3","source":"paper System 60; canonical record DCB-LI... | {"record_id":"DCB-LIT-P4-025","problem":{"problem_id":"dcb_lit_p4_025","task_type":"safety","name":"DynaCertBench System 060 · DCB-LIT-P4-025 · ~\\texttt{S042}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.6*x1-0.1*x2+0.05*x3+u1, dx3/dt = x4+u2, dx4/dt = -0.8*x3-0.15*x4+0.05*x1+u3","source":"... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{4}$","$\\mathcal{X... |
DCB-LIT-P4-026 | 61 | safety | Safety verification | literature | 3 | continuous | dx1/dt = -0.5*x1+0.3*x2*sin(x3)-0.1*x1**(2)*x2, dx2/dt = -0.6*x2+0.5*x1*cos(x3)+0.15*x3**(2)*x1, dx3/dt = -0.7*x3-0.1*x3**(3) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3} \end{pmatrix} = \begin{pmatrix} -0.5\,x_{1} + 0.3\,x_{2}\,\sin(x_{3}) - 0.1\,x_{1}^{2}\,x_{2}\\ -0.6\,x_{2} + 0.5\,x_{1}\,\cos(x_{3}) + 0.15\,x_{3}^{2}\,x_{1}\\ -0.7\,x_{3} - 0.1\,x_{3}^{3} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_026","task_type":"safety","name":"DynaCertBench System 061 · DCB-LIT-P4-026 · ~\\texttt{S048}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.5*x1+0.3*x2*sin(x3)-0.1*x1**(2)*x2, dx2/dt = -0.6*x2+0.5*x1*cos(x3)+0.15*x3**(2)*x1, dx3/dt = -0.7*x3-0.1*x3**(3)","source":"paper System 61; c... | {"record_id":"DCB-LIT-P4-026","problem":{"problem_id":"dcb_lit_p4_026","task_type":"safety","name":"DynaCertBench System 061 · DCB-LIT-P4-026 · ~\\texttt{S048}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.5*x1+0.3*x2*sin(x3)-0.1*x1**(2)*x2, dx2/dt = -0.6*x2+0.5*x1*cos(x3)+0.15*x3**(2)*x1, dx3/dt = -0.7*x3-0... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-027 | 62 | safety | Safety verification | literature | 3 | continuous | dx1/dt = x2+u0, dx2/dt = x3+u1, dx3/dt = -6*x3-2.92*x2-1.2*x1+x1**(2)+u2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3} \end{pmatrix} = \begin{pmatrix} x_{2} + u_{0}\\ x_{3} + u_{1}\\ -6\,x_{3} - 2.92\,x_{2} - 1.2\,x_{1} + x_{1}^{2} + u_{2} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_027","task_type":"safety","name":"DynaCertBench System 062 · DCB-LIT-P4-027 · ~\\texttt{S052}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = x3+u1, dx3/dt = -6*x3-2.92*x2-1.2*x1+x1**(2)+u2","source":"paper System 62; canonical record DCB-LIT-P4-027","assumptions":["Deter... | {"record_id":"DCB-LIT-P4-027","problem":{"problem_id":"dcb_lit_p4_027","task_type":"safety","name":"DynaCertBench System 062 · DCB-LIT-P4-027 · ~\\texttt{S052}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = x3+u1, dx3/dt = -6*x3-2.92*x2-1.2*x1+x1**(2)+u2","source":"paper System 62; canonical reco... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-028 | 63 | safety | Safety verification | literature | 2 | continuous | dx1/dt = -x1+0.08*x2+x1**(2)*x2+u0, dx2/dt = 0.6-0.08*x2-x1**(2)*x2+u1 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2} \end{pmatrix} = \begin{pmatrix} -x_{1} + 0.08\,x_{2} + x_{1}^{2}\,x_{2} + u_{0}\\ 0.6 - 0.08\,x_{2} - x_{1}^{2}\,x_{2} + u_{1} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_028","task_type":"safety","name":"DynaCertBench System 063 · DCB-LIT-P4-028 · ~\\texttt{S057}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -x1+0.08*x2+x1**(2)*x2+u0, dx2/dt = 0.6-0.08*x2-x1**(2)*x2+u1","source":"paper System 63; canonical record DCB-LIT-P4-028","assumptions":["Determi... | {"record_id":"DCB-LIT-P4-028","problem":{"problem_id":"dcb_lit_p4_028","task_type":"safety","name":"DynaCertBench System 063 · DCB-LIT-P4-028 · ~\\texttt{S057}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -x1+0.08*x2+x1**(2)*x2+u0, dx2/dt = 0.6-0.08*x2-x1**(2)*x2+u1","source":"paper System 63; canonical record... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{2}$","$\\mathcal{X... |
DCB-LIT-P4-029 | 64 | safety | Safety verification | literature | 3 | continuous | dx1/dt = x2+u0, dx2/dt = -0.1*x1-0.05*x2+0.02*x1*x3+u1, dx3/dt = -0.2*x3+0.1*x1+u2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3} \end{pmatrix} = \begin{pmatrix} x_{2} + u_{0}\\ -0.1\,x_{1} - 0.05\,x_{2} + 0.02\,x_{1}\,x_{3} + u_{1}\\ -0.2\,x_{3} + 0.1\,x_{1} + u_{2} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_029","task_type":"safety","name":"DynaCertBench System 064 · DCB-LIT-P4-029 · ~\\texttt{S058}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.1*x1-0.05*x2+0.02*x1*x3+u1, dx3/dt = -0.2*x3+0.1*x1+u2","source":"paper System 64; canonical record DCB-LIT-P4-029","assumption... | {"record_id":"DCB-LIT-P4-029","problem":{"problem_id":"dcb_lit_p4_029","task_type":"safety","name":"DynaCertBench System 064 · DCB-LIT-P4-029 · ~\\texttt{S058}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.1*x1-0.05*x2+0.02*x1*x3+u1, dx3/dt = -0.2*x3+0.1*x1+u2","source":"paper System 64; cano... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-030 | 65 | safety | Safety verification | literature | 3 | continuous | dx1/dt = -0.25*x1-x2**(2)-x3**(2)+0.75+u0, dx2/dt = -x2+x1*x3+u1, dx3/dt = -x3+x1*x2-0.1*x1+u2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3} \end{pmatrix} = \begin{pmatrix} -0.25\,x_{1} - x_{2}^{2} - x_{3}^{2} + 0.75 + u_{0}\\ -x_{2} + x_{1}\,x_{3} + u_{1}\\ -x_{3} + x_{1}\,x_{2} - 0.1\,x_{1} + u_{2} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_030","task_type":"safety","name":"DynaCertBench System 065 · DCB-LIT-P4-030 · ~\\texttt{S059}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.25*x1-x2**(2)-x3**(2)+0.75+u0, dx2/dt = -x2+x1*x3+u1, dx3/dt = -x3+x1*x2-0.1*x1+u2","source":"paper System 65; canonical record DCB-LIT-P4-030"... | {"record_id":"DCB-LIT-P4-030","problem":{"problem_id":"dcb_lit_p4_030","task_type":"safety","name":"DynaCertBench System 065 · DCB-LIT-P4-030 · ~\\texttt{S059}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.25*x1-x2**(2)-x3**(2)+0.75+u0, dx2/dt = -x2+x1*x3+u1, dx3/dt = -x3+x1*x2-0.1*x1+u2","source":"paper Sys... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-031 | 66 | safety | Safety verification | literature | 2 | continuous | dx1/dt = x1*(x1-0.1)*(1-x1)-0.3*x1*x2+u0, dx2/dt = -0.2*x2+0.1*x1*x2+u1 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2} \end{pmatrix} = \begin{pmatrix} x_{1}\,(x_{1} - 0.1)\,(1 - x_{1}) - 0.3\,x_{1}\,x_{2} + u_{0}\\ -0.2\,x_{2} + 0.1\,x_{1}\,x_{2} + u_{1} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_031","task_type":"safety","name":"DynaCertBench System 066 · DCB-LIT-P4-031 · ~\\texttt{S060}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x1*(x1-0.1)*(1-x1)-0.3*x1*x2+u0, dx2/dt = -0.2*x2+0.1*x1*x2+u1","source":"paper System 66; canonical record DCB-LIT-P4-031","assumptions":["Determ... | {"record_id":"DCB-LIT-P4-031","problem":{"problem_id":"dcb_lit_p4_031","task_type":"safety","name":"DynaCertBench System 066 · DCB-LIT-P4-031 · ~\\texttt{S060}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x1*(x1-0.1)*(1-x1)-0.3*x1*x2+u0, dx2/dt = -0.2*x2+0.1*x1*x2+u1","source":"paper System 66; canonical recor... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{2}$","$\\mathcal{X... |
DCB-LIT-P4-032 | 67 | safety | Safety verification | literature | 3 | continuous | dx1/dt = x2+u0, dx2/dt = -x1+x2*x3+u1, dx3/dt = 1-x2**(2)+u2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3} \end{pmatrix} = \begin{pmatrix} x_{2} + u_{0}\\ -x_{1} + x_{2}\,x_{3} + u_{1}\\ 1 - x_{2}^{2} + u_{2} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_032","task_type":"safety","name":"DynaCertBench System 067 · DCB-LIT-P4-032 · ~\\texttt{S062}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -x1+x2*x3+u1, dx3/dt = 1-x2**(2)+u2","source":"paper System 67; canonical record DCB-LIT-P4-032","assumptions":["Deterministically... | {"record_id":"DCB-LIT-P4-032","problem":{"problem_id":"dcb_lit_p4_032","task_type":"safety","name":"DynaCertBench System 067 · DCB-LIT-P4-032 · ~\\texttt{S062}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -x1+x2*x3+u1, dx3/dt = 1-x2**(2)+u2","source":"paper System 67; canonical record DCB-LIT-P... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-033 | 68 | safety | Safety verification | literature | 3 | continuous | dx1/dt = x3+x2*x1+u0, dx2/dt = -x2-x1**(2)+u1, dx3/dt = -x1-0.5*x3+u2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3} \end{pmatrix} = \begin{pmatrix} x_{3} + x_{2}\,x_{1} + u_{0}\\ -x_{2} - x_{1}^{2} + u_{1}\\ -x_{1} - 0.5\,x_{3} + u_{2} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_033","task_type":"safety","name":"DynaCertBench System 068 · DCB-LIT-P4-033 · ~\\texttt{S076}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x3+x2*x1+u0, dx2/dt = -x2-x1**(2)+u1, dx3/dt = -x1-0.5*x3+u2","source":"paper System 68; canonical record DCB-LIT-P4-033","assumptions":["Determin... | {"record_id":"DCB-LIT-P4-033","problem":{"problem_id":"dcb_lit_p4_033","task_type":"safety","name":"DynaCertBench System 068 · DCB-LIT-P4-033 · ~\\texttt{S076}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x3+x2*x1+u0, dx2/dt = -x2-x1**(2)+u1, dx3/dt = -x1-0.5*x3+u2","source":"paper System 68; canonical record ... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-034 | 69 | safety | Safety verification | literature | 4 | continuous | dx1/dt = x2+u0, dx2/dt = -0.8*x1-0.3*x2*(1+x1**(2))+0.1*x3+u1, dx3/dt = x4+u2, dx4/dt = -0.9*x3-0.25*x4*(1+x3**(2))+0.1*x1+u3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3}\\ \dot{x}_{4} \end{pmatrix} = \begin{pmatrix} x_{2} + u_{0}\\ -0.8\,x_{1} - 0.3\,x_{2}\,(1 + x_{1}^{2}) + 0.1\,x_{3} + u_{1}\\ x_{4} + u_{2}\\ -0.9\,x_{3} - 0.25\,x_{4}\,(1 + x_{3}^{2}) + 0.1\,x_{1} + u_{3} \end{pmat... | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_034","task_type":"safety","name":"DynaCertBench System 069 · DCB-LIT-P4-034 · ~\\texttt{S077}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.8*x1-0.3*x2*(1+x1**(2))+0.1*x3+u1, dx3/dt = x4+u2, dx4/dt = -0.9*x3-0.25*x4*(1+x3**(2))+0.1*x1+u3","source":"paper System 69; c... | {"record_id":"DCB-LIT-P4-034","problem":{"problem_id":"dcb_lit_p4_034","task_type":"safety","name":"DynaCertBench System 069 · DCB-LIT-P4-034 · ~\\texttt{S077}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.8*x1-0.3*x2*(1+x1**(2))+0.1*x3+u1, dx3/dt = x4+u2, dx4/dt = -0.9*x3-0.25*x4*(1+x3**(2))... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{4}$","$\\mathcal{X... |
DCB-LIT-P4-035 | 70 | safety | Safety verification | literature | 2 | discrete | x1[k+1] = -1/100*x2, x2[k+1] = 1/100*x1 | The update map is: \[ \mathbf{x}_{k+1} = \begin{pmatrix} x_{1,k+1}\\ x_{2,k+1} \end{pmatrix} = \begin{pmatrix} x_{1,k} + 0.01\,(-100\,x_{1,k} - 1\,x_{2,k})\\ x_{2,k} + 0.01\,(1\,x_{1,k} - 100\,x_{2,k}) \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_035","task_type":"safety","name":"DynaCertBench System 070 · DCB-LIT-P4-035 · ~\\texttt{S087}, \\cite{taheri2025barrierbench}","dynamics":"x1[k+1] = -1/100*x2, x2[k+1] = 1/100*x1","formal_domain":"unbounded","initial_set":{"type":"box","bounds":[["1/10","2/5"],["1/10","11/20"]]},"unsafe_set":{... | {"record_id":"DCB-LIT-P4-035","problem":{"problem_id":"dcb_lit_p4_035","task_type":"safety","name":"DynaCertBench System 070 · DCB-LIT-P4-035 · ~\\texttt{S087}, \\cite{taheri2025barrierbench}","dynamics":"x1[k+1] = -1/100*x2, x2[k+1] = 1/100*x1","formal_domain":"unbounded","initial_set":{"type":"box","bounds":[["1/10",... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{2}$","$\\mathcal{X... |
DCB-LIT-P4-036 | 71 | safety | Safety verification | literature | 4 | continuous | dx1/dt = -0.5*x1+0.3*x2, dx2/dt = -0.4*x2+0.15*cos(x1)*sin(x3), dx3/dt = -0.6*x3+0.1*sin(x2)*cos(x4), dx4/dt = -0.5*x4 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3}\\ \dot{x}_{4} \end{pmatrix} = \begin{pmatrix} -0.5\,x_{1} + 0.3\,x_{2}\\ -0.4\,x_{2} + 0.15\,\cos(x_{1})\,\sin(x_{3})\\ -0.6\,x_{3} + 0.1\,\sin(x_{2})\,\cos(x_{4})\\ -0.5\,x_{4} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_036","task_type":"safety","name":"DynaCertBench System 071 · DCB-LIT-P4-036 · ~\\texttt{U000}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.5*x1+0.3*x2, dx2/dt = -0.4*x2+0.15*cos(x1)*sin(x3), dx3/dt = -0.6*x3+0.1*sin(x2)*cos(x4), dx4/dt = -0.5*x4","source":"paper System 71; canonica... | {"record_id":"DCB-LIT-P4-036","problem":{"problem_id":"dcb_lit_p4_036","task_type":"safety","name":"DynaCertBench System 071 · DCB-LIT-P4-036 · ~\\texttt{U000}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.5*x1+0.3*x2, dx2/dt = -0.4*x2+0.15*cos(x1)*sin(x3), dx3/dt = -0.6*x3+0.1*sin(x2)*cos(x4), dx4/dt = -0.5... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{4}$","$\\mathcal{X... |
DCB-LIT-P4-037 | 72 | safety | Safety verification | literature | 3 | continuous | dx1/dt = -0.3*x1+0.5*sin(x2), dx2/dt = -0.4*x2-0.6*sin(x1)+0.1*sin(x3), dx3/dt = -0.5*x3+0.2*sin(x1)*sin(x2) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3} \end{pmatrix} = \begin{pmatrix} -0.3\,x_{1} + 0.5\,\sin(x_{2})\\ -0.4\,x_{2} - 0.6\,\sin(x_{1}) + 0.1\,\sin(x_{3})\\ -0.5\,x_{3} + 0.2\,\sin(x_{1})\,\sin(x_{2}) \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_037","task_type":"safety","name":"DynaCertBench System 072 · DCB-LIT-P4-037 · ~\\texttt{U001}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.3*x1+0.5*sin(x2), dx2/dt = -0.4*x2-0.6*sin(x1)+0.1*sin(x3), dx3/dt = -0.5*x3+0.2*sin(x1)*sin(x2)","source":"paper System 72; canonical record D... | {"record_id":"DCB-LIT-P4-037","problem":{"problem_id":"dcb_lit_p4_037","task_type":"safety","name":"DynaCertBench System 072 · DCB-LIT-P4-037 · ~\\texttt{U001}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.3*x1+0.5*sin(x2), dx2/dt = -0.4*x2-0.6*sin(x1)+0.1*sin(x3), dx3/dt = -0.5*x3+0.2*sin(x1)*sin(x2)","sour... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-038 | 73 | safety | Safety verification | literature | 3 | continuous | dx1/dt = -0.3*x1+0.2*sin(x2)*exp(-x3**(2)), dx2/dt = -0.4*x2+0.15*cos(x1)*exp(-x1**(2)), dx3/dt = -0.5*x3+0.1*sin(x1+x2) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3} \end{pmatrix} = \begin{pmatrix} -0.3\,x_{1} + 0.2\,\sin(x_{2})\,\exp(-x_{3}^{2})\\ -0.4\,x_{2} + 0.15\,\cos(x_{1})\,\exp(-x_{1}^{2})\\ -0.5\,x_{3} + 0.1\,\sin(x_{1} + x_{2}) \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_038","task_type":"safety","name":"DynaCertBench System 073 · DCB-LIT-P4-038 · ~\\texttt{U002}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.3*x1+0.2*sin(x2)*exp(-x3**(2)), dx2/dt = -0.4*x2+0.15*cos(x1)*exp(-x1**(2)), dx3/dt = -0.5*x3+0.1*sin(x1+x2)","source":"paper System 73; canoni... | {"record_id":"DCB-LIT-P4-038","problem":{"problem_id":"dcb_lit_p4_038","task_type":"safety","name":"DynaCertBench System 073 · DCB-LIT-P4-038 · ~\\texttt{U002}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.3*x1+0.2*sin(x2)*exp(-x3**(2)), dx2/dt = -0.4*x2+0.15*cos(x1)*exp(-x1**(2)), dx3/dt = -0.5*x3+0.1*sin(x... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-039 | 74 | safety | Safety verification | literature | 3 | discrete | x1[k+1] = 4/5*x1 + 1/10*sin(x2), x2[k+1] = 17/20*x2 + 2/25*x1*x3, x3[k+1] = 9/10*x3 + 2/25*cos(x1*x2) | The update map is: \[ \mathbf{x}_{k+1} = \begin{pmatrix} x_{1,k+1}\\ x_{2,k+1}\\ x_{3,k+1} \end{pmatrix} = \begin{pmatrix} 0.8\,x_{1,k} + 0.1\,\sin(x_{2,k})\\ 0.85\,x_{2,k} + 0.08\,x_{1,k}\,x_{3,k}\\ 0.9\,x_{3,k} + 0.08\,\cos(x_{1,k}\,x_{2,k}) \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_039","task_type":"safety","name":"DynaCertBench System 074 · DCB-LIT-P4-039 · ~\\texttt{U003}, \\cite{taheri2025barrierbench}","dynamics":"x1[k+1] = 4/5*x1 + 1/10*sin(x2), x2[k+1] = 17/20*x2 + 2/25*x1*x3, x3[k+1] = 9/10*x3 + 2/25*cos(x1*x2)","formal_domain":"unbounded","initial_set":{"type":"b... | {"record_id":"DCB-LIT-P4-039","problem":{"problem_id":"dcb_lit_p4_039","task_type":"safety","name":"DynaCertBench System 074 · DCB-LIT-P4-039 · ~\\texttt{U003}, \\cite{taheri2025barrierbench}","dynamics":"x1[k+1] = 4/5*x1 + 1/10*sin(x2), x2[k+1] = 17/20*x2 + 2/25*x1*x3, x3[k+1] = 9/10*x3 + 2/25*cos(x1*x2)","formal_doma... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-040 | 75 | safety | Safety verification | literature | 4 | continuous | dx1/dt = -0.65*x1 + 0.1*x2**2*cos(x3), dx2/dt = -0.7*x2 + 0.12*sin(x1)*tanh(x4), dx3/dt = -0.75*x3 + 0.08*x1*x2, dx4/dt = -0.6*x4 + 0.06*(x1 + x2) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3}\\ \dot{x}_{4} \end{pmatrix} = \begin{pmatrix} -0.65\,x_{1} + 0.1\,x_{2}^{2}\,\cos(x_{3})\\ -0.7\,x_{2} + 0.12\,\sin(x_{1})\,\tanh(x_{4})\\ -0.75\,x_{3} + 0.08\,x_{1}\,x_{2}\\ -0.6\,x_{4} + 0.06\,(x_{1} + x_{2}) \end{... | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_040","task_type":"safety","name":"DynaCertBench System 075 · DCB-LIT-P4-040 · ~\\texttt{U004}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.65*x1 + 0.1*x2**2*cos(x3), dx2/dt = -0.7*x2 + 0.12*sin(x1)*tanh(x4), dx3/dt = -0.75*x3 + 0.08*x1*x2, dx4/dt = -0.6*x4 + 0.06*(x1 + x2)","initia... | {"record_id":"DCB-LIT-P4-040","problem":{"problem_id":"dcb_lit_p4_040","task_type":"safety","name":"DynaCertBench System 075 · DCB-LIT-P4-040 · ~\\texttt{U004}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.65*x1 + 0.1*x2**2*cos(x3), dx2/dt = -0.7*x2 + 0.12*sin(x1)*tanh(x4), dx3/dt = -0.75*x3 + 0.08*x1*x2, dx... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{4}$","$\\mathcal{X... |
DCB-LIT-P4-041 | 76 | safety | Safety verification | literature | 3 | continuous | dx1/dt = -0.58*x1+0.12*sin(x2)*cos(x3), dx2/dt = -0.62*x2+0.1*exp(-x1**(2))*tanh(x3), dx3/dt = -0.66*x3+0.08*sin(x1*x2)*exp(-x3**(2)) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3} \end{pmatrix} = \begin{pmatrix} -0.58\,x_{1} + 0.12\,\sin(x_{2})\,\cos(x_{3})\\ -0.62\,x_{2} + 0.1\,\exp(-x_{1}^{2})\,\tanh(x_{3})\\ -0.66\,x_{3} + 0.08\,\sin(x_{1}x_{2})\,\exp(-x_{3}^{2}) \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_041","task_type":"safety","name":"DynaCertBench System 076 · DCB-LIT-P4-041 · ~\\texttt{U005}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.58*x1+0.12*sin(x2)*cos(x3), dx2/dt = -0.62*x2+0.1*exp(-x1**(2))*tanh(x3), dx3/dt = -0.66*x3+0.08*sin(x1*x2)*exp(-x3**(2))","source":"paper Syst... | {"record_id":"DCB-LIT-P4-041","problem":{"problem_id":"dcb_lit_p4_041","task_type":"safety","name":"DynaCertBench System 076 · DCB-LIT-P4-041 · ~\\texttt{U005}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.58*x1+0.12*sin(x2)*cos(x3), dx2/dt = -0.62*x2+0.1*exp(-x1**(2))*tanh(x3), dx3/dt = -0.66*x3+0.08*sin(x1... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-042 | 77 | safety | Safety verification | literature | 3 | continuous | dx1/dt = u0*cos(x3), dx2/dt = u0*sin(x3), dx3/dt = u1 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3} \end{pmatrix} = \begin{pmatrix} u_{0}\cos(x_{3})\\ u_{0}\sin(x_{3})\\ u_{1} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_042","task_type":"safety","name":"DynaCertBench System 077 · DCB-LIT-P4-042 · ~\\texttt{U006}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = u0*cos(x3), dx2/dt = u0*sin(x3), dx3/dt = u1","source":"paper System 77; canonical record DCB-LIT-P4-042","assumptions":["Deterministically normal... | {"record_id":"DCB-LIT-P4-042","problem":{"problem_id":"dcb_lit_p4_042","task_type":"safety","name":"DynaCertBench System 077 · DCB-LIT-P4-042 · ~\\texttt{U006}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = u0*cos(x3), dx2/dt = u0*sin(x3), dx3/dt = u1","source":"paper System 77; canonical record DCB-LIT-P4-042",... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-043 | 78 | safety | Safety verification | literature | 3 | discrete | x1[k+1] = 0.75*x1[k]+0.1*tanh(x2[k])*tanh(x3[k]), x2[k+1] = 0.82*x2[k]+0.09*sin(x1[k])*exp(-x3[k]**(2)), x3[k+1] = 0.79*x3[k]+0.08*cos(x1[k])*cos(x2[k]) | The update map is: \[ \mathbf{x}_{k+1} = \begin{pmatrix} x_{1,k+1}\\ x_{2,k+1}\\ x_{3,k+1} \end{pmatrix} = \begin{pmatrix} 0.75\,x_{1,k} + 0.1\,\tanh(x_{2,k})\,\tanh(x_{3,k})\\ 0.82\,x_{2,k} + 0.09\,\sin(x_{1,k})\,\exp(-x_{3,k}^{2})\\ 0.79\,x_{3,k} + 0.08\,\cos(x_{1,k})\,\cos(x_{2,k}) \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_043","task_type":"safety","name":"DynaCertBench System 078 · DCB-LIT-P4-043 · ~\\texttt{U007}, \\cite{taheri2025barrierbench}","dynamics":"x1[k+1] = 0.75*x1[k]+0.1*tanh(x2[k])*tanh(x3[k]), x2[k+1] = 0.82*x2[k]+0.09*sin(x1[k])*exp(-x3[k]**(2)), x3[k+1] = 0.79*x3[k]+0.08*cos(x1[k])*cos(x2[k])","... | {"record_id":"DCB-LIT-P4-043","problem":{"problem_id":"dcb_lit_p4_043","task_type":"safety","name":"DynaCertBench System 078 · DCB-LIT-P4-043 · ~\\texttt{U007}, \\cite{taheri2025barrierbench}","dynamics":"x1[k+1] = 0.75*x1[k]+0.1*tanh(x2[k])*tanh(x3[k]), x2[k+1] = 0.82*x2[k]+0.09*sin(x1[k])*exp(-x3[k]**(2)), x3[k+1] = ... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-044 | 79 | safety | Safety verification | literature | 3 | discrete | x1[k+1] = 0.73*x1[k]+0.13*sin(x2[k])*tanh(x3[k]), x2[k+1] = 0.89*x2[k]+0.17*cos(x1[k]**(2))*exp(-x3[k]**(2)), x3[k+1] = 0.64*x3[k]+0.22*tanh(x1[k]*x2[k]) | The update map is: \[ \mathbf{x}_{k+1} = \begin{pmatrix} x_{1,k+1}\\ x_{2,k+1}\\ x_{3,k+1} \end{pmatrix} = \begin{pmatrix} 0.73\,x_{1,k} + 0.13\,\sin(x_{2,k})\,\tanh(x_{3,k})\\ 0.89\,x_{2,k} + 0.17\,\cos(x_{1,k}^{2})\,\exp(-x_{3,k}^{2})\\ 0.64\,x_{3,k} + 0.22\,\tanh(x_{1,k}\,x_{2,k}) \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_044","task_type":"safety","name":"DynaCertBench System 079 · DCB-LIT-P4-044 · ~\\texttt{U008}, \\cite{taheri2025barrierbench}","dynamics":"x1[k+1] = 0.73*x1[k]+0.13*sin(x2[k])*tanh(x3[k]), x2[k+1] = 0.89*x2[k]+0.17*cos(x1[k]**(2))*exp(-x3[k]**(2)), x3[k+1] = 0.64*x3[k]+0.22*tanh(x1[k]*x2[k])",... | {"record_id":"DCB-LIT-P4-044","problem":{"problem_id":"dcb_lit_p4_044","task_type":"safety","name":"DynaCertBench System 079 · DCB-LIT-P4-044 · ~\\texttt{U008}, \\cite{taheri2025barrierbench}","dynamics":"x1[k+1] = 0.73*x1[k]+0.13*sin(x2[k])*tanh(x3[k]), x2[k+1] = 0.89*x2[k]+0.17*cos(x1[k]**(2))*exp(-x3[k]**(2)), x3[k+... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-LIT-P4-045 | 80 | safety | Safety verification | literature | 3 | continuous | dx1/dt = -0.62*x1+0.1*sin(x2+x3), dx2/dt = -0.67*x2+0.08*cos(x1)*exp(-x3**(2)), dx3/dt = -0.64*x3+0.09*tanh(x1)*sin(x2) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3} \end{pmatrix} = \begin{pmatrix} -0.62\,x_{1} + 0.1\,\sin(x_{2} + x_{3})\\ -0.67\,x_{2} + 0.08\,\cos(x_{1})\,\exp(-x_{3}^{2})\\ -0.64\,x_{3} + 0.09\,\tanh(x_{1})\,\sin(x_{2}) \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_lit_p4_045","task_type":"safety","name":"DynaCertBench System 080 · DCB-LIT-P4-045 · ~\\texttt{U009}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.62*x1+0.1*sin(x2+x3), dx2/dt = -0.67*x2+0.08*cos(x1)*exp(-x3**(2)), dx3/dt = -0.64*x3+0.09*tanh(x1)*sin(x2)","source":"paper System 80; canonic... | {"record_id":"DCB-LIT-P4-045","problem":{"problem_id":"dcb_lit_p4_045","task_type":"safety","name":"DynaCertBench System 080 · DCB-LIT-P4-045 · ~\\texttt{U009}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = -0.62*x1+0.1*sin(x2+x3), dx2/dt = -0.67*x2+0.08*cos(x1)*exp(-x3**(2)), dx3/dt = -0.64*x3+0.09*tanh(x1)*sin... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{3}$","$\\mathcal{X... |
DCB-EXT-P1-001 | 81 | stability | Stability certification | extended | 2 | continuous | dx1/dt = -x1+x1*x2, dx2/dt = -x2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}\\ \dot{y} \end{pmatrix} = \begin{pmatrix} -x+xy\\ -y \end{pmatrix}. \] | [
"abate2021fossil"
] | {"problem_id":"dcb_ext_p1_001","task_type":"stability","name":"DynaCertBench System 081 · DCB-EXT-P1-001 · Extend-Table~1 row~1 (NonPoly0), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1+x1*x2, dx2/dt = -x2","source":"paper System 81; canonical record DCB-EXT-P1-001","assumptions":["Deterministically normalized from... | {"record_id":"DCB-EXT-P1-001","problem":{"problem_id":"dcb_ext_p1_001","task_type":"stability","name":"DynaCertBench System 081 · DCB-EXT-P1-001 · Extend-Table~1 row~1 (NonPoly0), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1+x1*x2, dx2/dt = -x2","source":"paper System 81; canonical record DCB-EXT-P1-001","assumpti... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0)$","$\\mathcal{N}=\\mathbb{R}^{2}$","Verified ty... |
DCB-EXT-P1-002 | 82 | stability | Stability certification | extended | 2 | continuous | dx1/dt = -x1**3+x2, dx2/dt = -x1-x2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} -x_1^3+x_2\\ -x_1-x_2 \end{pmatrix}. \] | [
"abate2021fossil"
] | {"problem_id":"dcb_ext_p1_002","task_type":"stability","name":"DynaCertBench System 082 · DCB-EXT-P1-002 · Extend-Table~1 row~6 (Poly2), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1**3+x2, dx2/dt = -x1-x2","source":"paper System 82; canonical record DCB-EXT-P1-002","assumptions":["Deterministically normalized from... | {"record_id":"DCB-EXT-P1-002","problem":{"problem_id":"dcb_ext_p1_002","task_type":"stability","name":"DynaCertBench System 082 · DCB-EXT-P1-002 · Extend-Table~1 row~6 (Poly2), \\cite{abate2021fossil}","dynamics":"dx1/dt = -x1**3+x2, dx2/dt = -x1-x2","source":"paper System 82; canonical record DCB-EXT-P1-002","assumpti... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0)$","$\\mathcal{N}=\\mathbb{R}^{2}$","Verified ty... |
DCB-EXT-P1-003 | 83 | stability | Stability certification | extended | 2 | continuous | dx1/dt = x2+u1, dx2/dt = u2+((3/20)*(981/100)*(1/2)*sin(x1)-(1/10)*x2)/((3/20)*(1/2)**2) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} x_2+u_1\\ u_2+\dfrac{mgL\sin(x_1)-bx_2}{mL^2} \end{pmatrix}, \] where $m=0.15$, $g=9.81$, $L=0.5$, and $b=0.1$. | [
"edwards2024fossil"
] | {"problem_id":"dcb_ext_p1_003","task_type":"stability","name":"DynaCertBench System 083 · DCB-EXT-P1-003 · Extend-Table~4 \\#2 (SineModel), \\cite{edwards2024fossil}","dynamics":"dx1/dt = x2+u1, dx2/dt = u2+((3/20)*(981/100)*(1/2)*sin(x1)-(1/10)*x2)/((3/20)*(1/2)**2)","source":"paper System 83; canonical record DCB-EXT... | {"record_id":"DCB-EXT-P1-003","problem":{"problem_id":"dcb_ext_p1_003","task_type":"stability","name":"DynaCertBench System 083 · DCB-EXT-P1-003 · Extend-Table~4 \\#2 (SineModel), \\cite{edwards2024fossil}","dynamics":"dx1/dt = x2+u1, dx2/dt = u2+((3/20)*(981/100)*(1/2)*sin(x1)-(1/10)*x2)/((3/20)*(1/2)**2)","source":"p... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0)$","$\\mathcal{N}=\\{\\mathbf{x}\\in\\mathbb{R}^... |
DCB-EXT-P2-001 | 84 | roa | Region-of-attraction verification | extended | 2 | continuous | dx1/dt = sin(x2), dx2/dt = u-cos(x2)/(1-x1) | The closed-loop vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2 \end{pmatrix} = \begin{pmatrix} \sin(x_2)\\ u-\dfrac{\cos(x_2)}{1-x_1} \end{pmatrix} \] | [
"zhou2022neural"
] | {"problem_id":"dcb_ext_p2_001","task_type":"roa","name":"DynaCertBench System 084 · DCB-EXT-P2-001 · Extend-Section~5.2 and Appendix~C.3.2, \\cite{zhou2022neural}","dynamics":"dx1/dt = sin(x2), dx2/dt = u-cos(x2)/(1-x1)","controller_parameters":"u","controller_observations":{"u":["x1","x2"]},"control_bounds":[[-5,5]],"... | {"record_id":"DCB-EXT-P2-001","problem":{"problem_id":"dcb_ext_p2_001","task_type":"roa","name":"DynaCertBench System 084 · DCB-EXT-P2-001 · Extend-Section~5.2 and Appendix~C.3.2, \\cite{zhou2022neural}","dynamics":"dx1/dt = sin(x2), dx2/dt = u-cos(x2)/(1-x1)","controller_parameters":"u","controller_observations":{"u":... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":2,"problem_name":"Region-of-attraction verification","raw_items_latex":["$x^\\star=(0,0)$","Original $\\mathcal{N}=\\{\\mathbf... |
DCB-EXT-P3-001 | 85 | invariant | Forward-invariant set synthesis | extended | 6 | continuous | dx1/dt = x4, dx2/dt = x5, dx3/dt = x6, dx4/dt = 9.81*sin(x3)+sin(x3)*u1, dx5/dt = -9.81+9.81*cos(x3)+cos(x3)*u1, dx6/dt = u2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4\\ \dot{x}_5\\ \dot{x}_6 \end{pmatrix} = \begin{pmatrix} x_4\\[1ex] x_5\\[1ex] x_6\\[1ex] 9.81\sin(x_3)+\sin(x_3)u_1\\[1ex] -9.81+9.81\cos(x_3)+\cos(x_3)u_1\\[1ex] u_2 \end{pmatrix}, \] where $\mathbf{u}=(u_1,u_... | [
"meng2024physics"
] | {"problem_id":"dcb_ext_p3_001","task_type":"invariant","name":"DynaCertBench System 085 · DCB-EXT-P3-001 · Extend--2D quadrotor, \\cite{meng2024physics}","dynamics":"dx1/dt = x4, dx2/dt = x5, dx3/dt = x6, dx4/dt = 9.81*sin(x3)+sin(x3)*u1, dx5/dt = -9.81+9.81*cos(x3)+cos(x3)*u1, dx6/dt = u2","source":"paper System 85; c... | {"record_id":"DCB-EXT-P3-001","problem":{"problem_id":"dcb_ext_p3_001","task_type":"invariant","name":"DynaCertBench System 085 · DCB-EXT-P3-001 · Extend--2D quadrotor, \\cite{meng2024physics}","dynamics":"dx1/dt = x4, dx2/dt = x5, dx3/dt = x6, dx4/dt = 9.81*sin(x3)+sin(x3)*u1, dx5/dt = -9.81+9.81*cos(x3)+cos(x3)*u1, d... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","unsafe_set_X_U"],"set_contract_complete":true},"problem":3,"problem_name":"Forward-invariant set synthesis","raw_items_latex":["$\\mathcal{X} = \\{x\\in\\mathbb{R}^{6}\\mid \\lVert ... |
DCB-EXT-P3-002 | 86 | invariant | Forward-invariant set synthesis | extended | 9 | continuous | dx1/dt = x4, dx2/dt = x5, dx3/dt = x6, dx4/dt = -9.81*sin(x8)-sin(x8)*u1, dx5/dt = 9.81*cos(x8)*sin(x7)+cos(x8)*sin(x7)*u1, dx6/dt = 9.81*cos(x8)*cos(x7)-9.81+cos(x8)*cos(x7)*u1, dx7/dt = u2, dx8/dt = u3, dx9/dt = u4 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4\\ \dot{x}_5\\ \dot{x}_6\\ \dot{x}_7\\ \dot{x}_8\\ \dot{x}_9 \end{pmatrix} = \begin{pmatrix} x_4\\[1ex] x_5\\[1ex] x_6\\[1ex] -9.81\sin(x_8)-\sin(x_8)u_1\\[1ex] 9.81\cos(x_8)\sin(x_7) +\cos(x_8)\sin(x_7)u_1\\[1e... | [
"meng2024physics"
] | {"problem_id":"dcb_ext_p3_002","task_type":"invariant","name":"DynaCertBench System 086 · DCB-EXT-P3-002 · Extend--3D quadrotor, \\cite{meng2024physics}","dynamics":"dx1/dt = x4, dx2/dt = x5, dx3/dt = x6, dx4/dt = -9.81*sin(x8)-sin(x8)*u1, dx5/dt = 9.81*cos(x8)*sin(x7)+cos(x8)*sin(x7)*u1, dx6/dt = 9.81*cos(x8)*cos(x7)-... | {"record_id":"DCB-EXT-P3-002","problem":{"problem_id":"dcb_ext_p3_002","task_type":"invariant","name":"DynaCertBench System 086 · DCB-EXT-P3-002 · Extend--3D quadrotor, \\cite{meng2024physics}","dynamics":"dx1/dt = x4, dx2/dt = x5, dx3/dt = x6, dx4/dt = -9.81*sin(x8)-sin(x8)*u1, dx5/dt = 9.81*cos(x8)*sin(x7)+cos(x8)*si... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","unsafe_set_X_U"],"set_contract_complete":true},"problem":3,"problem_name":"Forward-invariant set synthesis","raw_items_latex":["$\\mathcal{X} = \\{x\\in\\mathbb{R}^{9}\\mid \\lVert ... |
DCB-EXT-P4-001 | 87 | safety | Safety verification | extended | 4 | continuous | dx1/dt = x2+u0, dx2/dt = -0.95*sin(x1)-0.02*x2+0.01*x3+u1, dx3/dt = -0.1*x3+0.02*x1+u2, dx4/dt = -0.03*x4+0.01*x2+u3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3}\\ \dot{x}_{4} \end{pmatrix} = \begin{pmatrix} x_{2} + u_{0}\\ -0.95\,\sin(x_{1}) - 0.02\,x_{2} + 0.01\,x_{3} + u_{1}\\ -0.1\,x_{3} + 0.02\,x_{1} + u_{2}\\ -0.03\,x_{4} + 0.01\,x_{2} + u_{3} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_ext_p4_001","task_type":"safety","name":"DynaCertBench System 087 · DCB-EXT-P4-001 · Extend-\\texttt{S002}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.95*sin(x1)-0.02*x2+0.01*x3+u1, dx3/dt = -0.1*x3+0.02*x1+u2, dx4/dt = -0.03*x4+0.01*x2+u3","source":"paper System 87; cano... | {"record_id":"DCB-EXT-P4-001","problem":{"problem_id":"dcb_ext_p4_001","task_type":"safety","name":"DynaCertBench System 087 · DCB-EXT-P4-001 · Extend-\\texttt{S002}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.95*sin(x1)-0.02*x2+0.01*x3+u1, dx3/dt = -0.1*x3+0.02*x1+u2, dx4/dt = -0.03*x4+0.0... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{4}$","$\\mathcal{X... |
DCB-EXT-P4-002 | 88 | safety | Safety verification | extended | 2 | continuous | dx1/dt = x2+u0, dx2/dt = -0.3*x1-0.2*(1+cos(x1))*x2-0.1*x1**(3)+u1 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2} \end{pmatrix} = \begin{pmatrix} x_{2} + u_{0}\\ -0.3\,x_{1} - 0.2\,(1 + \cos(x_{1}))\,x_{2} - 0.1\,x_{1}^{3} + u_{1} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_ext_p4_002","task_type":"safety","name":"DynaCertBench System 088 · DCB-EXT-P4-002 · Extend-\\texttt{S011}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.3*x1-0.2*(1+cos(x1))*x2-0.1*x1**(3)+u1","source":"paper System 88; canonical record DCB-EXT-P4-002","assumptions":["Deter... | {"record_id":"DCB-EXT-P4-002","problem":{"problem_id":"dcb_ext_p4_002","task_type":"safety","name":"DynaCertBench System 088 · DCB-EXT-P4-002 · Extend-\\texttt{S011}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -0.3*x1-0.2*(1+cos(x1))*x2-0.1*x1**(3)+u1","source":"paper System 88; canonical reco... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{2}$","$\\mathcal{X... |
DCB-EXT-P4-003 | 89 | safety | Safety verification | extended | 4 | continuous | dx1/dt = x2+u0, dx2/dt = -x1-0.4*x2+0.15*sin(x3)+u1, dx3/dt = x4+u2, dx4/dt = -0.6*x3-0.3*x4+u3 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_{1}\\ \dot{x}_{2}\\ \dot{x}_{3}\\ \dot{x}_{4} \end{pmatrix} = \begin{pmatrix} x_{2} + u_{0}\\ -x_{1} - 0.4\,x_{2} + 0.15\,\sin(x_{3}) + u_{1}\\ x_{4} + u_{2}\\ -0.6\,x_{3} - 0.3\,x_{4} + u_{3} \end{pmatrix}. \] | [
"taheri2025barrierbench"
] | {"problem_id":"dcb_ext_p4_003","task_type":"safety","name":"DynaCertBench System 089 · DCB-EXT-P4-003 · Extend-\\texttt{S024}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -x1-0.4*x2+0.15*sin(x3)+u1, dx3/dt = x4+u2, dx4/dt = -0.6*x3-0.3*x4+u3","source":"paper System 89; canonical record DCB-EXT-... | {"record_id":"DCB-EXT-P4-003","problem":{"problem_id":"dcb_ext_p4_003","task_type":"safety","name":"DynaCertBench System 089 · DCB-EXT-P4-003 · Extend-\\texttt{S024}, \\cite{taheri2025barrierbench}","dynamics":"dx1/dt = x2+u0, dx2/dt = -x1-0.4*x2+0.15*sin(x3)+u1, dx3/dt = x4+u2, dx4/dt = -0.6*x3-0.3*x4+u3","source":"pa... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X} = \\mathbb{R}^{4}$","$\\mathcal{X... |
DCB-EXT-P4-004 | 90 | safety | Safety verification | extended | 8 | continuous | dx1/dt = x2, dx2/dt = x3, dx3/dt = x4, dx4/dt = x5, dx5/dt = x6, dx6/dt = x7, dx7/dt = x8, dx8/dt = -20*x8+170*x7+800*x6+2273*x5+3980*x4+4180*x3+2400*x2+576*x1+sin(omega*x1) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_0\\ \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4\\ \dot{x}_5\\ \dot{x}_6\\ \dot{x}_7 \end{pmatrix} = \begin{pmatrix} x_1\\ x_2\\ x_3\\ x_4\\ x_5\\ x_6\\ x_7\\ -\begin{aligned}[t] &20x_7+170x_6+800x_5+2273x_4\\[-0.15ex] &{}+3980x_3+4180x_2+2400x_1+... | [
"abate2021fossil"
] | {"problem_id":"dcb_ext_p4_004","task_type":"safety","name":"DynaCertBench System 090 · DCB-EXT-P4-004 · Extend--Hi-Ord8 with bounded sinusoidal disturbance, \\cite{abate2021fossil}","dynamics":"dx1/dt = x2, dx2/dt = x3, dx3/dt = x4, dx4/dt = x5, dx5/dt = x6, dx6/dt = x7, dx7/dt = x8, dx8/dt = -20*x8+170*x7+800*x6+2273*... | {"record_id":"DCB-EXT-P4-004","paper_system_number":90,"paper_system_label":"System 90","local_name":"S090__DCB-EXT-P4-004","problem":{"problem_id":"dcb_ext_p4_004","task_type":"safety","name":"DynaCertBench System 090 · DCB-EXT-P4-004 · Extend--Hi-Ord8 with bounded sinusoidal disturbance, \\cite{abate2021fossil}","dyn... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X}=[-2.2,2.2]^8$","$\\mathcal{X}_I=[... |
DCB-EXT-P4-005 | 91 | safety | Safety verification | extended | 10 | continuous | dx1/dt = -x1+1/2*x2-1/10*x9**2+sin(x2), dx2/dt = -1/2*x1-x2, dx3/dt = -x3+1/2*x4-1/10*x1**2+exp(-x3)-1, dx4/dt = -1/2*x3-x4, dx5/dt = -x5+1/2*x6+1/10*x7**2, dx6/dt = -1/2*x5-x6, dx7/dt = -x7+1/2*x8, dx8/dt = -1/2*x7-x8, dx9/dt = -x9+1/2*x10, dx10/dt = -1/2*x9-x10+1/10*x2**2 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4\\ \dot{x}_5\\ \dot{x}_6\\ \dot{x}_7\\ \dot{x}_8\\ \dot{x}_9\\ \dot{x}_{10} \end{pmatrix} = \begin{pmatrix} -x_1+0.5x_2-0.1x_9^2+\sin(x_2)\\ -0.5x_1-x_2\\ -x_3+0.5x_4-0.1x_1^2+e^{-x_3}-1\\ -0.5x_3-x_4\\ -x_5+0.5... | [
"liu2024tool"
] | {"problem_id":"dcb_ext_p4_005","task_type":"safety","name":"DynaCertBench System 091 · DCB-EXT-P4-005 · Safety extension of Example~5.4, \\cite{liu2024tool}","dynamics":"dx1/dt = -x1+1/2*x2-1/10*x9**2+sin(x2), dx2/dt = -1/2*x1-x2, dx3/dt = -x3+1/2*x4-1/10*x1**2+exp(-x3)-1, dx4/dt = -1/2*x3-x4, dx5/dt = -x5+1/2*x6+1/10*... | {"record_id":"DCB-EXT-P4-005","paper_system_number":91,"paper_system_label":"System 91","local_name":"S091__DCB-EXT-P4-005","problem":{"problem_id":"dcb_ext_p4_005","task_type":"safety","name":"DynaCertBench System 091 · DCB-EXT-P4-005 · Safety extension of Example~5.4, \\cite{liu2024tool}","dynamics":"dx1/dt = -x1+1/2... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","initial_set_X_I","unsafe_set_X_U"],"set_contract_complete":true},"problem":4,"problem_name":"Safety verification","raw_items_latex":["$\\mathcal{X}=[-1,1]^{10}$","$\\mathcal{X}_I=[-... |
DCB-OURS-P1-001 | 92 | stability | Stability certification | ours | 8 | continuous | dx1/dt = -3*x1+x2*cos(x1)/(1+x8**2), dx2/dt = -3*x2+x3*cos(x2)/(1+x1**2), dx3/dt = -3*x3+x4*cos(x3)/(1+x2**2), dx4/dt = -3*x4+x5*cos(x4)/(1+x3**2), dx5/dt = -3*x5+x6*cos(x1)/(1+x4**2), dx6/dt = -3*x6+x7*cos(x2)/(1+x5**2), dx7/dt = -3*x7+x8*cos(x3)/(1+x6**2), dx8/dt = -3*x8+x1*cos(x4)/(1+x7**2) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4\\ \dot{x}_5\\ \dot{x}_6\\ \dot{x}_7\\ \dot{x}_8 \end{pmatrix} = \begin{pmatrix} -3 x_1 + x_2 \frac{\cos x_1}{1 + x_8^2}\\[6pt] -3 x_2 + x_3 \frac{\cos x_2}{1 + x_1^2}\\[6pt] -3 x_3 + x_4 \frac{\cos x_3}{1 + x_2... | [] | {"problem_id":"dcb_ours_p1_001","task_type":"stability","name":"DynaCertBench System 092 · DCB-OURS-P1-001 · 8D Rational-Cosine Ring","dynamics":"dx1/dt = -3*x1+x2*cos(x1)/(1+x8**2), dx2/dt = -3*x2+x3*cos(x2)/(1+x1**2), dx3/dt = -3*x3+x4*cos(x3)/(1+x2**2), dx4/dt = -3*x4+x5*cos(x4)/(1+x3**2), dx5/dt = -3*x5+x6*cos(x1)/... | {"record_id":"DCB-OURS-P1-001","paper_system_number":92,"paper_system_label":"System 92","local_name":"S092__DCB-OURS-P1-001","problem":{"problem_id":"dcb_ours_p1_001","task_type":"stability","name":"DynaCertBench System 092 · DCB-OURS-P1-001 · 8D Rational-Cosine Ring","dynamics":"dx1/dt = -3*x1+x2*cos(x1)/(1+x8**2), d... | {"candidate":null,"completeness":{"flags":["source_label_missing"],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0,0,0,0,0,0,0)$","$\\mathcal... |
DCB-OURS-P1-002 | 93 | stability | Stability certification | ours | 7 | continuous | dx1/dt = -5*x1+x2*cos(x1)/(1+x7**2), dx2/dt = -(9/2)*x2+(6/5)*x4*sin(2*x2)/(1+2*x1**2), dx3/dt = -6*x3+(4/5)*x6*cos(x3/2)/(1+(3/2)*x2**2), dx4/dt = -(11/2)*x4+(3/2)*x7*sin((3/2)*x4)/(1+3*x3**2), dx5/dt = -5*x5+(9/10)*x1*cos(2*x5)/(1+(4/3)*x4**2), dx6/dt = -(9/2)*x6+(7/5)*x5*sin(x6/3)/(1+(5/2)*x5**2), dx7/dt = -6*x7+(1/... | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} -5x_1 + x_2\dfrac{\cos(x_1)}{1+x_7^2}\\[4pt] -\dfrac{9}{2}x_2 +\dfrac{6}{5}x_4\dfrac{\sin(2x_2)}{1+2x_1^2}\\[4pt] -6x_3 +\dfrac{4}{5}x_6\dfrac{\cos(x_3/2)} {1+\frac{3}{2}x_2^2}\\[4pt] -\dfrac{11}{2}x_4 +\dfrac{3}{2}x_7\dfrac{\sin(3x_4/2)} {1+3x_3^2}\\[4pt]... | [] | {"problem_id":"dcb_ours_p1_002","task_type":"stability","name":"DynaCertBench System 093 · DCB-OURS-P1-002 · 7D Heterogeneous Trigonometric-Rational Network","dynamics":"dx1/dt = -5*x1+x2*cos(x1)/(1+x7**2), dx2/dt = -(9/2)*x2+(6/5)*x4*sin(2*x2)/(1+2*x1**2), dx3/dt = -6*x3+(4/5)*x6*cos(x3/2)/(1+(3/2)*x2**2), dx4/dt = -(... | {"record_id":"DCB-OURS-P1-002","paper_system_number":93,"paper_system_label":"System 93","local_name":"S093__DCB-OURS-P1-002","problem":{"problem_id":"dcb_ours_p1_002","task_type":"stability","name":"DynaCertBench System 093 · DCB-OURS-P1-002 · 7D Heterogeneous Trigonometric-Rational Network","dynamics":"dx1/dt = -5*x1... | {"candidate":null,"completeness":{"flags":["source_label_missing"],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":1,"problem_name":"Stability certification","raw_items_latex":["$x^\\star=(0,0,0,0,0,0,0)$","$\\mathcal{N... |
DCB-OURS-P2-001 | 94 | roa | Region-of-attraction verification | ours | 10 | continuous | dx1/dt = -x1+1/4*x2+1/20*(x3/(1+x3**2)), dx2/dt = -x2+1/4*x3+1/20*(x4/(1+x4**2)), dx3/dt = -x3+1/4*x4+1/20*(x5/(1+x5**2)), dx4/dt = -x4+1/4*x5+1/20*(x6/(1+x6**2)), dx5/dt = -x5+1/4*x6+1/20*(x7/(1+x7**2)), dx6/dt = -x6+1/4*x7+1/20*(x8/(1+x8**2)), dx7/dt = -x7+1/4*x8+1/20*(x9/(1+x9**2)), dx8/dt = -x8+1/4*x9+1/20*(x10/(1+... | The vector flow field is \[ \dot{x}_i=-x_i+\frac{1}{4}x_{i+1}+\frac{1}{20}\frac{x_{i+2}}{1+x_{i+2}^2},\qquad i=1,\ldots,10, \] where the indices are interpreted cyclically, with $x_{11}=x_1$ and $x_{12}=x_2$. | [] | {"problem_id":"dcb_ours_p2_001","task_type":"roa","name":"DynaCertBench System 094 · DCB-OURS-P2-001 · Our cyclic ten-dimensional rational system","dynamics":"dx1/dt = -x1+1/4*x2+1/20*(x3/(1+x3**2)), dx2/dt = -x2+1/4*x3+1/20*(x4/(1+x4**2)), dx3/dt = -x3+1/4*x4+1/20*(x5/(1+x5**2)), dx4/dt = -x4+1/4*x5+1/20*(x6/(1+x6**2)... | {"record_id":"DCB-OURS-P2-001","paper_system_number":94,"paper_system_label":"System 94","local_name":"S094__DCB-OURS-P2-001","problem":{"problem_id":"dcb_ours_p2_001","task_type":"roa","name":"DynaCertBench System 094 · DCB-OURS-P2-001 · Our cyclic ten-dimensional rational system","dynamics":"dx1/dt = -x1+1/4*x2+1/20*... | {"candidate":null,"completeness":{"flags":["source_label_missing"],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","neighborhood_N"],"set_contract_complete":true},"problem":2,"problem_name":"Region-of-attraction verification","raw_items_latex":["$x^\\star=\\mathbf{0}\\in\\math... |
DCB-OURS-P2-002 | 95 | roa | Region-of-attraction verification | ours | 7 | continuous | dx1/dt = x2, dx2/dt = -(1/2)*x2-(3/2)*sin(x1)-sin(x1-x3)-(3/2)*sin(x1-x7), dx3/dt = x4, dx4/dt = -(1/2)*x4-(1/2)*sin(x3)-sin(x3-x1)-sin(x3-x5), dx5/dt = x6, dx6/dt = -(1/2)*x6-sin(x5)-sin(x5-x3)-(3/2)*sin(x5-x7), dx7/dt = -(1/5)*sin(x7)-(3/2)*sin(x7-x1)-(3/2)*sin(x7-x5) | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4\\ \dot{x}_5\\ \dot{x}_6\\ \dot{x}_7 \end{pmatrix} = \begin{pmatrix} x_2\\[1mm] -\dfrac12x_2-\dfrac32\sin x_1-\sin(x_1-x_3)-\dfrac32\sin(x_1-x_7)\\[2mm] x_4\\[1mm] -\dfrac12x_4-\dfrac12\sin x_3-\sin(x_3-x_1)-\si... | [] | {"problem_id":"dcb_ours_p2_002","task_type":"roa","name":"DynaCertBench System 095 · DCB-OURS-P2-002 · Seven-dimensional multi-machine swing system","dynamics":"dx1/dt = x2, dx2/dt = -(1/2)*x2-(3/2)*sin(x1)-sin(x1-x3)-(3/2)*sin(x1-x7), dx3/dt = x4, dx4/dt = -(1/2)*x4-(1/2)*sin(x3)-sin(x3-x1)-sin(x3-x5), dx5/dt = x6, dx... | {"record_id":"DCB-OURS-P2-002","paper_system_number":95,"paper_system_label":"System 95","local_name":"S095__DCB-OURS-P2-002","problem":{"problem_id":"dcb_ours_p2_002","task_type":"roa","name":"DynaCertBench System 095 · DCB-OURS-P2-002 · Seven-dimensional multi-machine swing system","dynamics":"dx1/dt = x2, dx2/dt = -... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","initial_set_X_I","neighborhood_N"],"set_contract_complete":true},"problem":2,"problem_name":"Region-of-attraction verification","raw_items_latex":["$x^\\star=(0,0,0,0,0,0,0)$","$\\mat... |
DCB-OURS-P2-003 | 96 | roa | Region-of-attraction verification | ours | 7 | continuous | dx1/dt = x2, dx2/dt = -2*x1/(1+x1**2)+(1/2)*x3-(3/10)*x2+(1/5)*x5, dx3/dt = x4, dx4/dt = (1/2)*x1-(3/2)*x3-sin(x3)-(1/5)*x4+(1/10)*x6, dx5/dt = -(1/2)*x5-(1/5)*x2+(1/10)*x6, dx6/dt = -(2/5)*x6-(1/10)*x5-(1/10)*x4+(1/10)*x7, dx7/dt = -(3/10)*x7-(1/10)*x6 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4\\ \dot{x}_5\\ \dot{x}_6\\ \dot{x}_7 \end{pmatrix} = \begin{pmatrix} x_2\\[1mm] -\dfrac{2x_1}{1+x_1^2}+\dfrac12x_3-0.3\,x_2+0.2\,x_5\\[2mm] x_4\\[1mm] \dfrac12x_1-\dfrac32x_3-\sin(x_3)-0.2\,x_4+0.1\,x_6\\[2mm] -... | [] | {"problem_id":"dcb_ours_p2_003","task_type":"roa","name":"DynaCertBench System 096 · DCB-OURS-P2-003 · Seven-dimensional coupled saturating oscillator","dynamics":"dx1/dt = x2, dx2/dt = -2*x1/(1+x1**2)+(1/2)*x3-(3/10)*x2+(1/5)*x5, dx3/dt = x4, dx4/dt = (1/2)*x1-(3/2)*x3-sin(x3)-(1/5)*x4+(1/10)*x6, dx5/dt = -(1/2)*x5-(1... | {"record_id":"DCB-OURS-P2-003","paper_system_number":96,"paper_system_label":"System 96","local_name":"S096__DCB-OURS-P2-003","problem":{"problem_id":"dcb_ours_p2_003","task_type":"roa","name":"DynaCertBench System 096 · DCB-OURS-P2-003 · Seven-dimensional coupled saturating oscillator","dynamics":"dx1/dt = x2, dx2/dt ... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["equilibrium","initial_set_X_I","neighborhood_N"],"set_contract_complete":true},"problem":2,"problem_name":"Region-of-attraction verification","raw_items_latex":["$x^\\star=(0,0,0,0,0,0,0)$","$\\mat... |
DCB-OURS-P3-001 | 97 | invariant | Forward-invariant set synthesis | ours | 6 | continuous | dx1/dt = x2+u0, dx2/dt = -x1-1/10*sin(x1)-x2+x3, dx3/dt = -2*x3+x4, dx4/dt = -3/2*x4+x5, dx5/dt = -2*x5+x6, dx6/dt = -3/2*x6+u1 | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4\\ \dot{x}_5\\ \dot{x}_6 \end{pmatrix} = \begin{pmatrix} x_2+u_0\\[1mm] -x_1-\dfrac1{10}\sin(x_1)-x_2+x_3\\[2mm] -2x_3+x_4\\[1mm] -\dfrac32x_4+x_5\\[2mm] -2x_5+x_6\\[1mm] -\dfrac32x_6+u_1 \end{pmatrix}. \] | [] | {"problem_id":"dcb_ours_p3_001","task_type":"invariant","name":"DynaCertBench System 097 · DCB-OURS-P3-001 · New-6D Sin Cascade Invariance","dynamics":"dx1/dt = x2+u0, dx2/dt = -x1-1/10*sin(x1)-x2+x3, dx3/dt = -2*x3+x4, dx4/dt = -3/2*x4+x5, dx5/dt = -2*x5+x6, dx6/dt = -3/2*x6+u1","source":"paper System 97; canonical re... | {"record_id":"DCB-OURS-P3-001","paper_system_number":97,"paper_system_label":"System 97","local_name":"S097__DCB-OURS-P3-001","problem":{"problem_id":"dcb_ours_p3_001","task_type":"invariant","name":"DynaCertBench System 097 · DCB-OURS-P3-001 · New-6D Sin Cascade Invariance","dynamics":"dx1/dt = x2+u0, dx2/dt = -x1-1/1... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","unsafe_set_X_U"],"set_contract_complete":true},"problem":3,"problem_name":"Forward-invariant set synthesis","raw_items_latex":["$\\mathcal X=[-1,1]^6$","$\\mathcal X_{\\mathrm{seed}... |
DCB-OURS-P3-002 | 98 | invariant | Forward-invariant set synthesis | ours | 6 | continuous | dx1/dt = x2+u, dx2/dt = -x1-1/20*(exp(x1)-exp(-x1))-x2+x3, dx3/dt = -2*x3+x4, dx4/dt = -3/2*x4+x5, dx5/dt = -2*x5+x6, dx6/dt = -3/2*x6 | The vector flow field is: \[ \dot{\mathbf{x}}= \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4\\ \dot{x}_5\\ \dot{x}_6 \end{pmatrix} = \begin{pmatrix} x_2+u\\[1mm] -x_1-\dfrac1{20}\left(\exp(x_1)-\exp(-x_1)\right)-x_2+x_3\\[2mm] -2x_3+x_4\\ -\dfrac32x_4+x_5\\ -2x_5+x_6\\ -\dfrac32x_6 \end{pmatrix}. \] | [] | {"problem_id":"dcb_ours_p3_002","task_type":"invariant","name":"DynaCertBench System 098 · DCB-OURS-P3-002 · New-6D Exponential Cascade Invariance","dynamics":"dx1/dt = x2+u, dx2/dt = -x1-1/20*(exp(x1)-exp(-x1))-x2+x3, dx3/dt = -2*x3+x4, dx4/dt = -3/2*x4+x5, dx5/dt = -2*x5+x6, dx6/dt = -3/2*x6","source":"paper System 9... | {"record_id":"DCB-OURS-P3-002","paper_system_number":98,"paper_system_label":"System 98","local_name":"S098__DCB-OURS-P3-002","problem":{"problem_id":"dcb_ours_p3_002","task_type":"invariant","name":"DynaCertBench System 098 · DCB-OURS-P3-002 · New-6D Exponential Cascade Invariance","dynamics":"dx1/dt = x2+u, dx2/dt = ... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","unsafe_set_X_U"],"set_contract_complete":true},"problem":3,"problem_name":"Forward-invariant set synthesis","raw_items_latex":["$\\mathcal X=[-1,1]^6$","$\\mathcal X_I=\\left\\{x\\i... |
DCB-OURS-P3-003 | 99 | invariant | Forward-invariant set synthesis | ours | 5 | continuous | dx1/dt = x2-1/2*x1, dx2/dt = -x1-x1/(5*(1+x1**2))-2*x2+x3/(10*(1+x3**2)), dx3/dt = x4-1/2*x3, dx4/dt = -x3-1/40*(exp(x3)-exp(-x3))-2*x4+1/5*x5, dx5/dt = -3/2*x5-1/10*x5**3+u | The vector flow field is: \[ \dot{\mathbf{x}} = \begin{pmatrix} \dot{x}_1\\ \dot{x}_2\\ \dot{x}_3\\ \dot{x}_4\\ \dot{x}_5 \end{pmatrix} = \begin{pmatrix} x_2-\dfrac12x_1\\[2mm] -x_1-\dfrac{x_1}{5(1+x_1^2)}-2x_2+\dfrac{x_3}{10(1+x_3^2)}\\[3mm] x_4-\dfrac12x_3\\[2mm] -x_3-\dfrac1{40}\left(\exp(x_3)-\exp(-x_3)\right)-2x_4... | [] | {"problem_id":"dcb_ours_p3_003","task_type":"invariant","name":"DynaCertBench System 099 · DCB-OURS-P3-003 · New-5D Mixed Nonlinear Cascade Invariance","dynamics":"dx1/dt = x2-1/2*x1, dx2/dt = -x1-x1/(5*(1+x1**2))-2*x2+x3/(10*(1+x3**2)), dx3/dt = x4-1/2*x3, dx4/dt = -x3-1/40*(exp(x3)-exp(-x3))-2*x4+1/5*x5, dx5/dt = -3/... | {"record_id":"DCB-OURS-P3-003","paper_system_number":99,"paper_system_label":"System 99","local_name":"S099__DCB-OURS-P3-003","problem":{"problem_id":"dcb_ours_p3_003","task_type":"invariant","name":"DynaCertBench System 099 · DCB-OURS-P3-003 · New-5D Mixed Nonlinear Cascade Invariance","dynamics":"dx1/dt = x2-1/2*x1, ... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","unsafe_set_X_U"],"set_contract_complete":true},"problem":3,"problem_name":"Forward-invariant set synthesis","raw_items_latex":["$\\mathcal X=[-1,1]^5$","$\\mathcal X_U=\\left\\{x\\i... |
DCB-OURS-P3-004 | 100 | invariant | Forward-invariant set synthesis | ours | 6 | discrete | x1[k+1] = x1+1/4*(tanh(x2-x1) + tanh(x3-x1)), x2[k+1] = x2+1/4*(tanh(x1-x2) + tanh(x3-x2) + tanh(x4-x2)), x3[k+1] = x3+1/4*(tanh(x1-x3) + tanh(x2-x3) + tanh(x5-x3)), x4[k+1] = x4+1/4*(tanh(x2-x4) + tanh(x5-x4)), x5[k+1] = x5+1/4*(tanh(x3-x5) + tanh(x4-x5) + tanh(x6-x5)), x6[k+1] = x6+1/4*(tanh(x5-x6)) | Consider an undirected network $\mathcal G=(\mathcal V,\mathcal E)$ with $N=6$ nodes and adjacency matrix \[ A= \begin{pmatrix} 0&1&1&0&0&0\\ 1&0&1&1&0&0\\ 1&1&0&0&1&0\\ 0&1&0&0&1&0\\ 0&0&1&1&0&1\\ 0&0&0&0&1&0 \end{pmatrix}, \] where $A_{ij}=1$ means that nodes $i$ and $j$ are connected. The discrete-time dynamics are ... | [] | {"problem_id":"dcb_ours_p3_004","task_type":"invariant","name":"DynaCertBench System 100 · DCB-OURS-P3-004 · New-6D Opinion Dynamics","dynamics":"x1[k+1] = x1+1/4*(tanh(x2-x1) + tanh(x3-x1)), x2[k+1] = x2+1/4*(tanh(x1-x2) + tanh(x3-x2) + tanh(x4-x2)), x3[k+1] = x3+1/4*(tanh(x1-x3) + tanh(x2-x3) + tanh(x5-x3)), x4[k+1] ... | {"record_id":"DCB-OURS-P3-004","paper_system_number":100,"paper_system_label":"System 100","local_name":"S100__DCB-OURS-P3-004","problem":{"problem_id":"dcb_ours_p3_004","task_type":"invariant","name":"DynaCertBench System 100 · DCB-OURS-P3-004 · New-6D Opinion Dynamics","dynamics":"x1[k+1] = x1+1/4*(tanh(x2-x1) + tanh... | {"candidate":null,"completeness":{"flags":[],"llm_input_ready":true,"missing_required_set_roles":[],"required_set_roles":["state_space_X","unsafe_set_X_U"],"set_contract_complete":true},"problem":3,"problem_name":"Forward-invariant set synthesis","raw_items_latex":["$\\mathcal X=[-1,1]^6$","$\\mathcal X_U=\\{x\\in\\mat... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.