$\operatorname{Inst}(\emptyset)$

$\prod_{s=1}^{t}2^{p_{s}-1}$

${\rm D}_{\rm NP}\leq_{0\hbox{-}T}{\rm D}_{\rm P}$

$\p^{A}=\np^{A}$

$\p^{L}=\p$

$\langle M^{\prime},\epsilon\rangle$

$\np^{\mathcal{O}}$

$\langle M,1^{n},1^{t}\rangle\in{\rm U}_{\rm NP}$

$\np^{L}=\np$

$x\notin{\rm HP}$

$\np^{\p}=\np$

$\p$

$A\leq_{f(n)\hbox{-}T}B$

${\rm D}_{\rm NP}\not\in\p^{{\rm D}_{\rm P}}$

$x\in\mathcal{O}$

$L\in{\rm\Sigma_{1}^{0}}$

$n,t\in{\mathbb{N}^{+}}$

$t^{\prime}\in{\mathbb{N}}$

$\Theta(2^{n})$

${\rm D}_{\rm NP}=\{\langle M,1^{n}\rangle\mid n\in{\mathbb{N}}\land(\exists x% \in\{0,1\}^{n})[M$

$\langle M,1^{n}\rangle\in{\rm D}_{\rm NP}$

${\rm U}_{\rm P}=\{\langle M,x,1^{t}\rangle\mid t\in{\mathbb{N}^{+}}\land M$

$M^{\mathcal{O}}$

${\rm HP}=\{\langle M,w\rangle\mid M\text{ halts on input }w\}.$

$(\forall x)[x\in A\iff f(x)\in B]$

$z\notin{\rm D}_{\rm NP}$

$(\forall L\in{\rm\Sigma_{1}^{0}})[L\leq_{m}A]$

$\p^{\p}=\p$

$A\leq_{m}B$

${\mathbb{N}^{+}}=\{1,2,3,\ldots\}$

${\rm D}_{\rm NP}\in{\rm\Sigma_{1}^{0}}$

$\Omega(2^{n})$

$\p^{X}\neq\np^{X}$

$\p^{A}\neq\np^{A}\iff\p\neq\np$

$\p\neq\np$

$]\}$

${\rm U}_{\rm NP}$

$L\leq_{m}{\rm D}_{\rm NP}$

$x]\}$

$\p^{\mathcal{O}}$

$\min(c,2^{n})$

${\rm D}_{\rm NP}\leq_{m}{\rm D}_{\rm P}$

$z\not\in{\rm D}_{\rm NP}$

$y=\epsilon$

$\p^{\p}$

${\rm U}_{\rm P}$

$\{0,1\}^{n}\cap L(M)$

$A\leq_{T}B$

${\rm D}_{\rm P}$

$U_{\text{\bf P}}$

${\rm PSPACE}$

$x\in L(M)$

$\p^{B}\neq\np^{B}$

$A\in\p$

$\langle M,x\rangle\in{\rm D}_{\rm P}\iff(\exists t>0)[\langle M,x,1^{t}\rangle% \in{\rm U}_{\rm P}]$

${\mathbb{N}}=\{0,1,2,\ldots\}$

$A=L(M^{B})$

$\mathcal{C}^{\mathcal{D}}=\bigcup_{A\in\mathcal{D}}\mathcal{C}^{A}$

$\np$

${\rm U}_{\rm NP}\not\in\p^{{\rm U}_{\rm P}}$

$\np^{\p}$

$f:{\mathbb{N}}\rightarrow{\mathbb{N}}$

$\p=\np$

$f(x)\in{\rm D}_{\rm NP}$

${\rm\Sigma_{0}^{0}}$

${\rm\Sigma_{0}^{0}}^{\mathcal{O}}$

$A\in{\rm\Sigma_{1}^{0}}$

$x\not\in\mathcal{O}$

$\p^{A}=\p$

${\rm U}_{\rm NP}=\{\langle M,1^{n},1^{t}\rangle\mid n\in{\mathbb{N}}\land t\in% {\mathbb{N}^{+}}\land(\exists x\in\{0,1\}^{n})[M$

$\langle M,1^{n}\rangle$

$x\in{\rm HP}$

$\langle M,1^{n}\rangle\in{\rm D}_{\rm NP}\iff(\exists t>0)[\langle M,1^{n},1^{% t}\rangle\in{\rm U}_{\rm NP}]$

$x\}$

$w\in\{0,1\}^{n}$

$\epsilon\notin L(M^{\prime})$

$A\leq_{1\hbox{-}T}B$

${\rm HP}\leq_{m}{\rm D}_{\rm NP}$

$\np^{A}=\np$

$(\forall x)[x\notin{\rm HP}\implies f(x)\notin{\rm D}_{\rm NP}]$

${\rm\Sigma_{1}^{0}}$

${\rm HP}$

$\langle M,w\rangle$

$(\forall x)[x\in{\rm HP}\iff f(x)\in{\rm D}_{\rm NP}]$

$\mathcal{C},\mathcal{D}$

$\epsilon\in L(M^{\prime})$

${\rm D}_{\rm NP}$

${\rm D}_{\rm NP}\leq_{h\hbox{-}T}{\rm D}_{\rm P}$

$L\in\p$

${\rm D}_{\rm P}=\{\langle M,x\rangle\mid M$

${\rm D}_{\rm NP}\leq_{1\hbox{-}T}{\rm D}_{\rm P}$

$c\in{\mathbb{N}^{+}}$

$(S^{\prime}\setminus\{x,y\})\cup\{v^{xy}\}$

$G\setminus X:=G[V(G)\setminus X]$

$V(C_{2})$

$p_{j}\in B$

$H\setminus u$

$\chi(G)\leq k$

$u\in V(H)$

$\{\overline{K_{2}\cup C_{2k+1}}\mid k\in\mathbb{N}\}$