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49bd51c36e5209f42bf61207e15cddf8d3270470 | subsection | 453 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | Base case:
this holds by tr:mo-t-s-b.
Inductive case:
By tr:mo-t-s, \mathit {{\color {CarnationPink}{M;\overline{H}\rightsquigarrow M^{\prime \prime }}}} holds by IH, we need to prove \mathit {{\color {CarnationPink}{M^{\prime \prime };H\rightsquigarrow M^{\prime }}}}.
By tr:mo-t-2 e need to prove that THMR: \exists \m... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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eead8b3705009e71d12a7fc901ac7776b1c0b7fd | subsection | 454 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | By this and tr:ok-mon (adjusted for \mathit {{\color {CarnationPink}{L^{I}}}}) we have that
HPHR \forall {{\color {black}{\mathtt {mon\text{-}care}(}}\mathsf {{\color {RoyalBlue}{H}}},\mathsf {{\color {RoyalBlue}{\Delta }}}{{\color {black}{)}}}} \operatorname{{\color {black}{\approx _{\varphi }}}}{{\color {black}{\math... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
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c16bd7ba53ab87f2fc0a2de1e950a52acb4bbddb | subsection | 455 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | (\mathit {{\color {CarnationPink}{\sigma }}}, {{\color {black}{\mathtt {mon\text{-}care}(}}\mathit {{\color {CarnationPink}{H}}},\mathit {{\color {CarnationPink}{H_0}}}{{\color {black}{)}}}}, \mathit {{\color {CarnationPink}{\sigma ^{\prime }}}}) \in \mathit {{\color {CarnationPink}{\rightsquigarrow }}}, so this case h... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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2b72c27ca54d84115a1df983cebf5af01417ad92 | subsection | 456 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | \\
\text{ if }
&\ \mathsf {{\color {RoyalBlue}{C, H\triangleright \Pi \rho }}} \mathsf {{\color {RoyalBlue}{~\mathrel {\xrightarrow{}}~}}} \mathsf {{\color {RoyalBlue}{C, H^{\prime }\triangleright \Pi ^{\prime }\rho ^{\prime }}}}
\\
&\ \mathit {{\color {CarnationPink}{C,H\triangleright {\color {black}{\left.\mathsf {{\... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
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d6f0342a8cde995e19b9a41dcc46ca95eaf6b3fa | subsection | 457 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | \spadesuit
Lemma 27 (\mathbf {{\color {RedOrange}{L^{P}}}} Attacker actions preserve \operatorname{{\color {black}{\mathrel {\hbox{$\sim $}\vspace{-1.48752pt}\hbox{$\sim $}\vspace{-1.48752pt}\hbox{$\sim $}}}}})
&
\forall ... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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f2da084b9a9f68f78afe9d9f4942f5df2b5185d0 | subsection | 458 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | \\
\text{ if }
&\ \mathsf {{\color {RoyalBlue}{C, H\triangleright \Pi \rho }}} \mathsf {{\color {RoyalBlue}{~\mathrel {\xrightarrow{}}~}}} \mathsf {{\color {RoyalBlue}{C, H^{\prime }\triangleright \Pi ^{\prime }\rho ^{\prime }}}}
\\
&\ \mathit {{\color {CarnationPink}{C,H\triangleright \Pi \rho }}} \mathit {{\color {Ca... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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abdee3ab0d2dc3f215b55abe6b55822c4be1a524 | subsection | 459 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | Suppose this does not hold by contradiction, there can be one clause that does not hold based on tr:state-rel-proof:
two related high-locations \mathsf {{\color {RoyalBlue}{\ell }}} and \mathit {{\color {CarnationPink}{n}}} point to unrelated values.
Two cases arise: creation and update of a location to an unrelated v... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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2733f7221ab2602c7a516c19fda7e94fb1b26ba6 | subsection | 460 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | \mathit {Components}~\mathsf {{\color {RoyalBlue}{C}}} \mathrel {::=}&\ \mathsf {{\color {RoyalBlue}{\overline{F} ; \overline{I} ; \overline{E}}}}
\\
\mathit {Exports}~\mathsf {{\color {RoyalBlue}{E}}} \mathrel {::=}&\ \mathsf {{\color {RoyalBlue}{f}}}
\\
\mathit {Expressions}~\mathsf {{\color {RoyalBlue}{e}}} \mathrel... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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bf7df2c404490e898e29648ed72f0d15752610a6 | subsection | 461 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | The Target Language \mathbf {{\color {RedOrange}{L^{P}}}}
Syntax Changes
\mathit {Components}~\mathbf {{\color {RedOrange}{C}}} \mathrel {::=}&\ \mathbf {{\color {RedOrange}{\overline{F} ; \overline{I}; \overline{E} ; k_{root}, k_{com}}}}
\\
\mathit {Exports}~\mathbf {{\color {RedOrange}{E}}} \mathrel {::=}&\ \mathbf ... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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62ce2d0cc597af1315a567b2b15534adf7d195ae | subsection | 462 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | The former is used to create a part of the heap for component-managed datastructures.
The latter does not even hide a location, we need it as a placeholder.
Traces in this case have the same syntactic structure as before, but they do not carry the whole heap.
So we use a different symbol (\mathbf {{\color {RedOrange}{\... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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9d426ca6a58743515ca060d78bc271e37071a315 | subsection | 463 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | Semantics Changes
In \mathbf {{\color {RedOrange}{L^{P}}}} we need functionality to tell if a pair is a location or not and to traverse values in order to extract such locations.
{\color {RedOrange}{L^{P}}}-isloc\endcsname \begin{array}{c}\textsf {\scriptsize ({\mathbf {{\color {RedOrange}{L^{P}}}}-isloc})} \\ {
(\math... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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3c816a7683dffdf4ecaa3b81560fb5b4383e99a4 | subsection | 464 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | However, the compiler will ensure that the context only receives \mathbf {{\color {RedOrange}{k_{com}}}} as a capability and never a newly-allocated capability. | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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12a120327e9e97a93ce9adc0eb1011d3b675ceab | subsection | 465 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | So the context will not be able to test equality of capabilities generated by the compiled component as it will effectively see only one.
{\color {RedOrange}{L^{P}}}-eqcap-true\endcsname \begin{array}{c}\textsf {\scriptsize ({\mathbf {{\color {RedOrange}{L^{P}}}}-eqcap-true})} \\ {
\mathbf {{\color {RedOrange}{H\triang... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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f7fd49117f2ccc77ba0744c1995278ca0dcdc87b | subsection | 466 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | Property 1 (Heap locations)
AS mentioned, the trace semantics carries the whole shared heap: locations created by the compiled component and then passed to the context and locations created by the context and passed to the compiled component.
We can really partition the heap as follows then:
[Table: NO_CAPTION]
Now, f... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1007/978-3-540-31987-0_29",
"end": 2050,
"openalex_id": "https://openalex.org/W2134056477",
"raw": "Alan Jeffrey and Julian Rathke. Java Jr.: Fully abstract trace semantics for a core Java language. In ESOP'05, volume 3444 of LNCS, pages... | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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a2b03dbb902b137819b870133efd9bdb370441ab | subsection | 467 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | \Box
Lemma 29 (Completeness)
\text{if }
&
\mathbf {{\color {RedOrange}{\mathbf {{\color {RedOrange}{\mathsf {TR}^{}_{}\left(C_1\right)}}}=\mathbf {{\color {RedOrange}{\mathsf {TR}^{}_{}\left(C_2\right)}}}}}}
\\
\text{then }
&
\mathbf {{\color {RedOrange}{C_1 \operatorname{\mathbf {{\color {RedOrange}{\operatorname{\m... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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e078f8e96a483a239a512a1015f478edaca87ba0 | subsection | 468 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | \Box
Lemma 30 (Full abstraction of the trace semantics for compiled components)
\mathbf {{\color {RedOrange}{\mathbf {{\color {RedOrange}{\mathsf {TR}^{}_{}\left({\color {black}{\left.\mathsf {{\color {RoyalBlue}{\fbox{$\mathsf {{\color {RoyalBlue}{C_1}}}$}}}} \right.^{\mathsf {{\color {RoyalBlue}{L^{U}}}}}_{\mathbf ... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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37837fab265f51a4e51657fba66ff7a4c65d9f63 | subsection | 469 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | The Compiler {\color {black}{\left.\mathsf {{\color {RoyalBlue}{\fbox{$\mathsf {{\color {RoyalBlue}{\cdot }}}$}}}} \right.^{\mathsf {{\color {RoyalBlue}{L^{U}}}}}_{\mathbf {{\color {RedOrange}{L^{P}}}}}}}
{\color {black}{\left.\mathsf {{\color {RoyalBlue}{\fbox{
$\mathsf {{\color {RoyalBlue}{\overline{F} ; \overline{... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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374e95168f7b7b3858068d30223c07beab3c05a0 | subsection | 470 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | The compiled code will maintain the following invariant:
no locations (even though protected by capabilities) are ever made accessible “in clear” to the context;
“made accessible” means either passed as a parameter or through a shared location;
instead, before passing control to the context, all component-created lo... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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9a87b2f8f8fa14015c66c600f8d73bc36a9cfca6 | subsection | 471 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | This is where we need to use \mathbf {{\color {RedOrange}{k_{com}}}} as leaking different capabilities would lead to differentiation between components.
Fortunately, the context starts execution and, in order to call the compiled component, it must allocate at least one location, so this problem cannot arise.
Syntacti... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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654edf4e311fd218cddf42f9b53b35a4687151de | subsection | 472 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | Support Functions
Read
\mathbf {{\color {RedOrange}{s_{read}}}} =&\ \begin{aligned}
&
\mathbf {{\color {RedOrange}{let}}}~\mathbf {{\color {RedOrange}{x_{n}}}}\mathbf {{\color {RedOrange}{=}}}\mathbf {{\color {RedOrange}{x.1.1}}}~\mathbf {{\color {RedOrange}{in}}}~
\\
&\ \mathbf {{\color {RedOrange}{let}}}~\mathbf {{\... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.018260056152939796,
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-0.026329871267080307,
0.0027554072439670563,... | |
e558d784aeec5818514fca4ec971a21a894df55c | subsection | 473 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | Write
\mathbf {{\color {RedOrange}{s_{write}}}} =&\ \begin{aligned}
&
\mathbf {{\color {RedOrange}{let}}}~\mathbf {{\color {RedOrange}{x_{n}}}}\mathbf {{\color {RedOrange}{=}}}\mathbf {{\color {RedOrange}{x.1.1}}}~\mathbf {{\color {RedOrange}{in}}}~
\\
&\ \mathbf {{\color {RedOrange}{let}}}~\mathbf {{\color {RedOrange... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.010862505994737148,
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0.0021644916851073503,
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0.0... | |
aed73fa84bbc77b47cdb27d1406bc454f8486cd9 | subsection | 474 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | We want to keep the value passed as parameter \mathbf {{\color {RedOrange}{x}}} unchanged but replace its subvalues that are pairs and, more specifically, component-created locations, with a pair with its location masked to be the index in the list of component-allocated locations.
This can be implemented by checking t... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.02925225719809532,
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0.01043742522597313,
... | |
1f2a52bf8bf72dd4039f1ac2e1f7ad52cd320cfe | subsection | 475 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | Registration
\mathbf {{\color {RedOrange}{s_{register}(x_{loc},x_{cap})}}} =&\ \begin{aligned}
&
\mathbf {{\color {RedOrange}{\overline{K}::x_{cap};}}}
\end{aligned}
This statement registers capability \mathbf {{\color {RedOrange}{x_{cap}}}} in the list of component-created capabilities.
Preamble
The preamble is res... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.007269496563822031,
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... | |
ea7c32122236c528c0f7a8a9f0de4392c11c283d | subsection | 476 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | \mathbf {{\color {RedOrange}{s_{post}(x)}}} =&\ \begin{aligned}
&
\forall \mathbf {{\color {RedOrange}{\left\langle n,k\right\rangle }}}\in {{\color {black}{\mathtt {reach}(}}\mathbf {{\color {RedOrange}{\overline{S}}}}{{\color {black}{)}}}}.~ \mathbf {{\color {RedOrange}{isloc(\left\langle n,k\right\rangle )}}}
\\
& \... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.028295917436480522,
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0.0... | |
87b59b74c00f9174923384e95b130929f5e2f6dd | subsection | 477 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | The only additions are two functions \mathsf {{\color {RoyalBlue}{terminate}}} and \mathsf {{\color {RoyalBlue}{diverge}}}, which do what their name suggests:
&\mathsf {{\color {RoyalBlue}{terminate(x)\mapsto fail}}}
\\
&\mathsf {{\color {RoyalBlue}{diverge(x)\mapsto {call}~diverge~0}}}
The Common Prefix
\mathbf {{\... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.04590819403529167,
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... | |
31db77fef071d4a8670d9605ee0c1def20178d78 | subsection | 478 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | For all of its content \mathbf {{\color {RedOrange}{n\mapsto v:\eta }}}, we do a structural analysis of \mathbf {{\color {RedOrange}{v}}}.
This happens at the meta-level, in the backtranslation algorithm.
\mathbf {{\color {RedOrange}{v}}} may contain subvalues of the form \mathbf {{\color {RedOrange}{\left\langle i,k_{... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.04440885782241821,
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0.0... | |
a6b91e4331a840d51abcfd4631a43ecdc7a49c64 | subsection | 479 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | \mathsf {{\color {RoyalBlue}{\ell }}} is looked up as \mathsf {{\color {RoyalBlue}{B({\color {black}{\left\langle \!\left\langle {\mathbf {{\color {RedOrange}{\fbox{$\mathbf {{\color {RedOrange}{i}}}$}}}}} \right\rangle \!\right\rangle ^{\mathbf {{\color {RedOrange}{L^{P}}}}}_{\mathsf {{\color {RoyalBlue}{L^{U}}}}}}})}... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.059308551251888275,
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0.... | |
9fb58a9aba453e1085bfa5ce6b9ba7851338bc42 | subsection | 480 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | We consider \mathbf {{\color {RedOrange}{\alpha _1}}} to be the last action in the trace of {\color {black}{\left.\mathsf {{\color {RoyalBlue}{\mathsf {{\color {RoyalBlue}{C_1}}}}}} \right.^{\mathsf {{\color {RoyalBlue}{{S}}}}}_{}} while \mathbf {{\color {RedOrange}{\alpha _2}}} is the last one of {\color {black}{\left... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.039546992629766464,
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... | |
3387b72be3e3ab5f73fbc30a88095ace4f6ab172 | subsection | 481 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | \mathbf {{\color {RedOrange}{\alpha _1}}}= \mathbf {{\color {RedOrange}{\mathtt {call}~ f~ v~ H{!}}}} and \mathbf {{\color {RedOrange}{\alpha _2}}}= \mathbf {{\color {RedOrange}{\mathtt {call}~ f~ v~ H^{\prime }{!}}}}
Here few cases can arise, consider \mathbf {{\color {RedOrange}{H}}}=\mathbf {{\color {RedOrange}{H_1,... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.05221957713365555,
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0.... | |
1111499cd7a050b20b264a20242b378e9acc6b65 | subsection | 482 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | Code
\mathsf {{\color {RoyalBlue}{
\begin{aligned}&
\mathsf {{\color {RoyalBlue}{if}}}~\mathsf {{\color {RoyalBlue}{!\ell _i==i}}}~\mathsf {{\color {RoyalBlue}{then}}}~
\\
&\ \mathsf {{\color {RoyalBlue}{let}}}~\mathsf {{\color {RoyalBlue}{x}}}\mathsf {{\color {RoyalBlue}{=}}}\mathsf {{\color {RoyalBlue}{L_{glob}({\co... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.04372208192944527,
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0... | |
f2ee1e6eb99fd1ee10a704213be114ad08329ab2 | subsection | 483 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | The code in this case must access the location related to \mathbf {{\color {RedOrange}{n}}}, it will get stuck in one case and succeed in the other:
\mathsf {{\color {RoyalBlue}{{if}~!\ell _i==i~{then}~ {let}~x=update({\color {black}{\left\langle \!\left\langle {\mathbf {{\color {RedOrange}{\fbox{$\mathbf {{\color {Red... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.0402568057179451,
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... | |
8d972ba21b78a8d28bcd39c96bdcff5bbe267f4d | subsection | 484 | 510 | Proof of thm:rsc-prf-eq (thm:rsc-prf-eq) | \mathbf {{\color {RedOrange}{\alpha _1}}}= \mathbf {{\color {RedOrange}{\mathtt {call}~ f~ v~ H{!}}}} and \mathbf {{\color {RedOrange}{\alpha _2}}}= \mathbf {{\color {RedOrange}{\mathbf {{\color {RedOrange}{\uparrow }}}}}}
Code \mathsf {{\color {RoyalBlue}{{if}~!\ell _i==i~{then}~{call}~terminate~0~{else}~\mathsf {{\co... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.04322296753525734,
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-0.009943420067429543,
0.044... | |
4df6389184457364f54c1b0ed11bec9e12ecf503 | subsection | 485 | 510 | A Fully Abstract Compiler from | We perform the aforementioned changes to languages. | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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0.... | |
85bbc11bedf8c0dd426cabac0644adba72bdc77e | subsection | 486 | 510 | Syntax Changes | \mathit {Components}~\mathbf {{\color {RedOrange}{C}}} \mathrel {::=}&\ \mathbf {{\color {RedOrange}{\overline{F} ; \overline{I}; \overline{E} ; k_{root}, k_{com}}}}
\\
\mathit {Exports}~\mathbf {{\color {RedOrange}{E}}} \mathrel {::=}&\ \mathbf {{\color {RedOrange}{f}}}
\\
\mathit {Expressions}~\mathbf {{\color {RedOr... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.028465591371059418,
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0.019399339333176613,
0.02446667291224003,
0.02... | |
e8018af5fe114abf7c216292fce99de809a63998 | subsection | 487 | 510 | Syntax Changes | The latter does not even hide a location, we need it as a placeholder.Traces in this case have the same syntactic structure as before, but they do not carry the whole heap.
So we use a different symbol (\mathbf {{\color {RedOrange}{\beta }}}), to visually distinguish between the two traces and the kind of information c... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.04016844555735588,
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0... | |
c45c83c08f460568cd4dfc1c5871f13a38f4f89a | subsection | 488 | 510 | Semantics Changes | In \mathbf {{\color {RedOrange}{L^{P}}}} we need functionality to tell if a pair is a location or not and to traverse values in order to extract such locations.{\color {RedOrange}{L^{P}}}-isloc\endcsname \begin{array}{c}\textsf {\scriptsize ({\mathbf {{\color {RedOrange}{L^{P}}}}-isloc})} \\ {
(\mathbf {{\color {RedOra... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.03389907628297806,
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0.... | |
57031cc303cafc04f14106209570f79581057392 | subsection | 489 | 510 | Semantics Changes | However, the compiler will ensure that the context only receives \mathbf {{\color {RedOrange}{k_{com}}}} as a capability and never a newly-allocated capability.
So the context will not be able to test equality of capabilities generated by the compiled component as it will effectively see only one.{\color {RedOrange}{L^... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.047304775565862656,
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0.... | |
36b741863186785052a9224467e0b3a0b3704371 | subsection | 490 | 510 | A Fully Abstract Trace Semantics for | \mathbf {{\color {RedOrange}{\Theta \xrightarrow{}\!\!\!\!\rightarrow \Theta ^{\prime }}}} &&& \text{State $\mathbf {{\color {RedOrange}{\Theta }}}$ emits visible action $\mathbf {{\color {RedOrange}{\beta }}}$ becoming $\mathbf {{\color {RedOrange}{\Theta ^{\prime }}}}$.}
\\
\mathbf {{\color {RedOrange}{\Theta {~\over... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.05249105393886566,
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0.027176328003406525,
0.0... | |
5340628067dea308100e890c02d9ffa57a289256 | subsection | 491 | 510 | Results about the Trace Semantics | The following results hold for \mathbf {{\color {RedOrange}{C_1}}}={\color {black}{\left.\mathsf {{\color {RoyalBlue}{\fbox{$\mathsf {{\color {RoyalBlue}{C_1}}}$}}}} \right.^{\mathsf {{\color {RoyalBlue}{L^{U}}}}}_{\mathbf {{\color {RedOrange}{L^{P}}}}}}} and \mathbf {{\color {RedOrange}{C_2}}}={\color {black}{\left.\m... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.04156051203608513,
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0.... | |
b81cc6c28662affb066b96bccebf0d724d6a36e8 | subsection | 492 | 510 | Results about the Trace Semantics | By contraposition:
\text{if }
&
\mathbf {{\color {RedOrange}{\mathbf {{\color {RedOrange}{\mathsf {TR}^{}_{}\left(C_1\right)}}}\ne \mathbf {{\color {RedOrange}{\mathsf {TR}^{}_{}\left(C_2\right)}}}}}}
\\
\text{then }
&
\mathbf {{\color {RedOrange}{\exists \mathbf {{\color {RedOrange}{A}}}.~ A\left[C_1\right]^{\mathbf ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1007/978-3-540-31987-0_29",
"end": 1115,
"openalex_id": "https://openalex.org/W2134056477",
"raw": "Alan Jeffrey and Julian Rathke. Java Jr.: Fully abstract trace semantics for a core Java language. In ESOP'05, volume 3444 of LNCS, pages... | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.02246280387043953,
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... | |
238754def6656005659343cf4f489761954d3df1 | subsection | 493 | 510 | Results about the Trace Semantics | The semantics forbids guessing, so a context will never have access to the locations that \mathbf {{\color {RedOrange}{C_1}}} or \mathbf {{\color {RedOrange}{C_2}}} do not share.
Thus a context can exhibit a difference in behaviour by relying on something that \mathbf {{\color {RedOrange}{C_1}}} modified unlike \mathbf... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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0.03... | |
95676e7a2eef94ca3f0282c41e8d53c0a145f7e8 | subsection | 494 | 510 | Results about the Trace Semantics | The Compiler {\color {black}{\left.\mathsf {{\color {RoyalBlue}{\fbox{$\mathsf {{\color {RoyalBlue}{\cdot }}}$}}}} \right.^{\mathsf {{\color {RoyalBlue}{L^{U}}}}}_{\mathbf {{\color {RedOrange}{L^{P}}}}}}}
{\color {black}{\left.\mathsf {{\color {RoyalBlue}{\fbox{
$\mathsf {{\color {RoyalBlue}{\overline{F} ; \overline{... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.08587812632322311,
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0.0024986749049276114,
-0.0035458295606076717,
-0.... | |
0ed6667fc58d3521780193fad5370cc50d358655 | subsection | 495 | 510 | Results about the Trace Semantics | The compiled code will maintain the following invariant:
no locations (even though protected by capabilities) are ever made accessible “in clear” to the context;
“made accessible” means either passed as a parameter or through a shared location;
instead, before passing control to the context, all component-created lo... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.004542535170912743,
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0.012494831345975399,
0.0403... | |
caa13bcff5b80cd2cef0c521004f8bc5bd4a6aaf | subsection | 496 | 510 | Results about the Trace Semantics | This is where we need to use \mathbf {{\color {RedOrange}{k_{com}}}} as leaking different capabilities would lead to differentiation between components.
Fortunately, the context starts execution and, in order to call the compiled component, it must allocate at least one location, so this problem cannot arise.
Syntacti... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.042849309742450714,
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0.01397027913480997,
0.0372... | |
c9ff19f386f11a128906cd882be9aef7499e67eb | subsection | 497 | 510 | Results about the Trace Semantics | Support Functions
Read
\mathbf {{\color {RedOrange}{s_{read}}}} =&\ \begin{aligned}
&
\mathbf {{\color {RedOrange}{let}}}~\mathbf {{\color {RedOrange}{x_{n}}}}\mathbf {{\color {RedOrange}{=}}}\mathbf {{\color {RedOrange}{x.1.1}}}~\mathbf {{\color {RedOrange}{in}}}~
\\
&\ \mathbf {{\color {RedOrange}{let}}}~\mathbf {{\... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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0.0027554072439670563,... | |
3a1375eb2a2e79f7db9d14b85104799a45ad2b34 | subsection | 498 | 510 | Results about the Trace Semantics | Write
\mathbf {{\color {RedOrange}{s_{write}}}} =&\ \begin{aligned}
&
\mathbf {{\color {RedOrange}{let}}}~\mathbf {{\color {RedOrange}{x_{n}}}}\mathbf {{\color {RedOrange}{=}}}\mathbf {{\color {RedOrange}{x.1.1}}}~\mathbf {{\color {RedOrange}{in}}}~
\\
&\ \mathbf {{\color {RedOrange}{let}}}~\mathbf {{\color {RedOrange... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.010862505994737148,
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0.0... | |
c902dbd161b8caf9e640910a7171d8f039bad8af | subsection | 499 | 510 | Results about the Trace Semantics | We want to keep the value passed as parameter \mathbf {{\color {RedOrange}{x}}} unchanged but replace its subvalues that are pairs and, more specifically, component-created locations, with a pair with its location masked to be the index in the list of component-allocated locations.
This can be implemented by checking t... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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... | |
b1fe2ab87dd40de76d8b151d8128660631a30cca | subsection | 500 | 510 | Results about the Trace Semantics | Registration
\mathbf {{\color {RedOrange}{s_{register}(x_{loc},x_{cap})}}} =&\ \begin{aligned}
&
\mathbf {{\color {RedOrange}{\overline{K}::x_{cap};}}}
\end{aligned}
This statement registers capability \mathbf {{\color {RedOrange}{x_{cap}}}} in the list of component-created capabilities.
Preamble
The preamble is res... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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... | |
31254334f02cdd965862ac643850b66e8855208a | subsection | 501 | 510 | Results about the Trace Semantics | \mathbf {{\color {RedOrange}{s_{post}(x)}}} =&\ \begin{aligned}
&
\forall \mathbf {{\color {RedOrange}{\left\langle n,k\right\rangle }}}\in {{\color {black}{\mathtt {reach}(}}\mathbf {{\color {RedOrange}{\overline{S}}}}{{\color {black}{)}}}}.~ \mathbf {{\color {RedOrange}{isloc(\left\langle n,k\right\rangle )}}}
\\
& \... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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0.0... | |
207fd107db19399a1382873b853165e0ab092d61 | subsection | 502 | 510 | Results about the Trace Semantics | The only additions are two functions \mathsf {{\color {RoyalBlue}{terminate}}} and \mathsf {{\color {RoyalBlue}{diverge}}}, which do what their name suggests:
&\mathsf {{\color {RoyalBlue}{terminate(x)\mapsto fail}}}
\\
&\mathsf {{\color {RoyalBlue}{diverge(x)\mapsto {call}~diverge~0}}}
The Common Prefix
\mathbf {{\... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.04590819403529167,
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... | |
8a2adfa31a9a73aecdf01cb8c68ac42b5b3760f5 | subsection | 503 | 510 | Results about the Trace Semantics | For all of its content \mathbf {{\color {RedOrange}{n\mapsto v:\eta }}}, we do a structural analysis of \mathbf {{\color {RedOrange}{v}}}.
This happens at the meta-level, in the backtranslation algorithm.
\mathbf {{\color {RedOrange}{v}}} may contain subvalues of the form \mathbf {{\color {RedOrange}{\left\langle i,k_{... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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0.0... | |
a003cfa7b85a7d43f50d57700f3a516a734988f1 | subsection | 504 | 510 | Results about the Trace Semantics | \mathsf {{\color {RoyalBlue}{\ell }}} is looked up as \mathsf {{\color {RoyalBlue}{B({\color {black}{\left\langle \!\left\langle {\mathbf {{\color {RedOrange}{\fbox{$\mathbf {{\color {RedOrange}{i}}}$}}}}} \right\rangle \!\right\rangle ^{\mathbf {{\color {RedOrange}{L^{P}}}}}_{\mathsf {{\color {RoyalBlue}{L^{U}}}}}}})}... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.059308551251888275,
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0.... | |
dad7078e956e6bc598ac448795bcf24a16566164 | subsection | 505 | 510 | Results about the Trace Semantics | We consider \mathbf {{\color {RedOrange}{\alpha _1}}} to be the last action in the trace of {\color {black}{\left.\mathsf {{\color {RoyalBlue}{\mathsf {{\color {RoyalBlue}{C_1}}}}}} \right.^{\mathsf {{\color {RoyalBlue}{{S}}}}}_{}} while \mathbf {{\color {RedOrange}{\alpha _2}}} is the last one of {\color {black}{\left... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.039546992629766464,
0.021131398156285286,
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... | |
0d1415be75de54acf6c8ce97212242573bc49cff | subsection | 506 | 510 | Results about the Trace Semantics | \mathbf {{\color {RedOrange}{\alpha _1}}}= \mathbf {{\color {RedOrange}{\mathtt {call}~ f~ v~ H{!}}}} and \mathbf {{\color {RedOrange}{\alpha _2}}}= \mathbf {{\color {RedOrange}{\mathtt {call}~ f~ v~ H^{\prime }{!}}}}
Here few cases can arise, consider \mathbf {{\color {RedOrange}{H}}}=\mathbf {{\color {RedOrange}{H_1,... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.05221957713365555,
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0.... | |
97bad96d9d338df7cff77017215d397e07189198 | subsection | 507 | 510 | Results about the Trace Semantics | Code
\mathsf {{\color {RoyalBlue}{
\begin{aligned}&
\mathsf {{\color {RoyalBlue}{if}}}~\mathsf {{\color {RoyalBlue}{!\ell _i==i}}}~\mathsf {{\color {RoyalBlue}{then}}}~
\\
&\ \mathsf {{\color {RoyalBlue}{let}}}~\mathsf {{\color {RoyalBlue}{x}}}\mathsf {{\color {RoyalBlue}{=}}}\mathsf {{\color {RoyalBlue}{L_{glob}({\co... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
-0.04372208192944527,
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0... | |
6a66e16c053af9ff25ec5eae883555988be196de | subsection | 508 | 510 | Results about the Trace Semantics | The code in this case must access the location related to \mathbf {{\color {RedOrange}{n}}}, it will get stuck in one case and succeed in the other:
\mathsf {{\color {RoyalBlue}{{if}~!\ell _i==i~{then}~ {let}~x=update({\color {black}{\left\langle \!\left\langle {\mathbf {{\color {RedOrange}{\fbox{$\mathbf {{\color {Red... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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... | |
dbebd28b61a2f0a780d4279dd30ec423ba92bcbb | subsection | 509 | 510 | Results about the Trace Semantics | \mathbf {{\color {RedOrange}{\alpha _1}}}= \mathbf {{\color {RedOrange}{\mathtt {call}~ f~ v~ H{!}}}} and \mathbf {{\color {RedOrange}{\alpha _2}}}= \mathbf {{\color {RedOrange}{\mathbf {{\color {RedOrange}{\uparrow }}}}}}
Code \mathsf {{\color {RoyalBlue}{{if}~!\ell _i==i~{then}~{call}~terminate~0~{else}~\mathsf {{\co... | {
"cite_spans": []
} | 1804.00489 | Robustly Safe Compilation or, Efficient, Provably Secure Compilation | [
"Marco Patrignani",
"Deepak Garg"
] | [
"cs.PL"
] | 2,018 | en | Computer Science | [
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bcccc44cbb3c6afad7f00b42dfbf11c80eabba28 | abstract | 0 | 129 | Abstract | Infrastructure systems are increasingly facing new security threats due to
the vulnerabilities of cyber-physical components that support their operation.
In this article, we investigate how the infrastructure operator (defender)
should prioritize the investment in securing a set of facilities in order to
reduce the imp... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
-0.02034025639295578,
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... | |
9a5d5d25071b26b9859ad29d41abd4ba3121ea8d | subsection | 1 | 129 | Introduction | In this article, we consider the problem of strategic allocation of defense effort to secure one or more facilities of an infrastructure system that is prone to a targeted attack by a malicious adversary. The setup is motivated by the recent incidents and projected threats to critical infrastructures such as transporta... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 377,
"openalex_id": "https://openalex.org/W2161400053",
"raw": "John Moteff and Paul Parfomak. Critical infrastructure and key assets: definition and identification. LIBRARY OF CONGRESS WASHINGTON DC CONGRESSIONAL RESEARCH SERVICE... | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
-0.010115791112184525,
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f3bc56b2d3266359d63b9277fdcebca75f25363c | subsection | 2 | 129 | Introduction | If the increase in the usage cost of a facility is larger than the cost of attack, then we say that it is a vulnerable facility.Our approach to characterizing Nash equilibrium (NE) of the normal form game is based on the fact that it is strategically equivalent to a zero-sum game. Hence, the set of attacker's equilibri... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1016/s0076-5392(08)x6169-7",
"end": 3350,
"openalex_id": "https://openalex.org/W1578630563",
"raw": "Tamer Başar and Geert Jan Olsder. Dynamic noncooperative game theory. SIAM, 1998.",
"source_ref_id": "3edd3ef301b1728a9f97c8c181ef... | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
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15673639c48357ff1406b5c6c58d138d439d5061 | subsection | 3 | 129 | Introduction | In contrast, our model considers multiple facilities, and assumes that both players have complete information of the usage cost of each facility.In fact, for our model, we are able to provide sharp conditions under which proactive defense strictly increases the defender's utility. Given any attack cost, unless the defe... | {
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"raw": "Mathieu Dahan and Saurabh Amin. Network flow routing under strategic link disruptions. In Communication, Control, and Computing (Allerto... | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
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610b29c16befcf662b900b4d3b65e976f98cd0ac | subsection | 4 | 129 | Attacker-Defender Interaction: Normal Form versus Sequential Games | Consider an infrastructure system modeled as a set of components (facilities) \mathcal {E}. To defend the system against an external malicious attack, the system operator (defender) can secure one or more facilities in \mathcal {E} by investing in appropriate security technology. The set of facilities in question can i... | {
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"source_ref_id": "23dc311e0d6cfbf10... | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
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90e5943a3479381e1421c2acba71d92eb67540cd | subsection | 5 | 129 | Attacker-Defender Interaction: Normal Form versus Sequential Games | In \Gamma , we denote the defender's mixed strategy as \sigma _d\stackrel{\Delta }{=}\left(\sigma _d(s_d)\right)_{s_d\in S_d} \in \Delta (S_d), where \sigma _d(s_d) is the probability that the set of secured facilities is s_d. Similarly, a mixed strategy of the attacker is \sigma _a\stackrel{\Delta }{=}\left(\sigma _a(... | {
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} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
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df3fecca86191187306981731c2037d867d48463 | subsection | 6 | 129 | Attacker-Defender Interaction: Normal Form versus Sequential Games | For a pure strategy profile \left(s_d, s_a\right), the utilities of defender and attacker can be respectively expressed as follows:u_d(s_d, s_a)&=-C(s_d, s_a)-p_d\cdot |s_d|, \quad u_a(s_d, s_a)=C(s_d, s_a)-p_a\cdot {1}\lbrace s_a\ne \emptyset \rbrace .For a mixed strategy profile \left(\sigma _d, \sigma _a\right), the... | {
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} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
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2faeacb6933798da9a4164eeda6a7cc6351d8327 | subsection | 7 | 129 | Attacker-Defender Interaction: Normal Form versus Sequential Games | A strategy profile \sigma ^*=(\sigma _d^*, \sigma _a^*) is a NE if:U_d(\sigma _d^*, \sigma _a^*) &\ge U_d(\sigma _d, \sigma _a^*), \quad \forall \sigma _d\in \Delta (S_d),\\
U_a(\sigma _d^*, \sigma _a^*) &\ge U_a(\sigma _d^*, \sigma _a), \quad \forall \sigma _a\in \Delta (S_a).In the sequential game \widetilde{\Gamma }... | {
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} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
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7b19bd2f7a3f7dae472ead11901f6e8c056fc216 | subsection | 8 | 129 | Model Discussion | One of our main assumptions is that the attacker's capability is limited to targeting at most one facility, while the defender can invest in securing multiple facilities. Although this assumption appears to be somewhat restrictive, it enables us to derive analytical results on the equilibrium structure for a system wit... | {
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"raw": "Marcin Dziubiński and Sanjeev Goyal. Network design and defence. Games and Economic Behavior, 79:30–43, 2013.",
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"Manxi Wu",
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fc6f30a8f0501ac83f927be873ccc1a188b1d6af | subsection | 9 | 129 | Model Discussion | This cost can be naturally evaluated as the user cost in a Wardrop equilibrium (), although socially optimal cost has also been considered in the literature ().Finally, we note that for the purpose of our analysis, the usage cost as given in (REF ) fully captures the impact of player' actions on the system. For any two... | {
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"raw": "Vicki M Bier and Kjell Hausken. Defending and attacking a network of two arcs subject to traffic congestion. Reliability Engineering & Syste... | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
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a8bef43f7dc0922a83e09f13c53256bff732bf77 | subsection | 10 | 129 | Rationalizable Strategies and Aggregate Defense Effort | We introduce two preliminary results that are useful in our subsequent analysis. Firstly, we show that the defender's strategy can be equivalently represented by a vector of facility-specific security effort levels. Secondly, we identify the set of rationalizable strategies of both players.For any defender's mixed stra... | {
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} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
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da9a69861d91bddbbbed19cf6f431214d36d2f90 | subsection | 11 | 129 | Rationalizable Strategies and Aggregate Defense Effort | The following defender's strategy is feasible and induces \rho :&\sigma _d(\left\lbrace e\in \mathcal {E}| \rho _e\ge \rho _{(i)}\right\rbrace )=\rho _{(i)}-\rho _{(i+1)}, \quad \forall i=1, \dots , m-1\\
&\sigma _d(\left\lbrace e\in \mathcal {E}| \rho _e\ge \rho _{(m)}\right\rbrace )= \rho _{(m)}, \\
&\sigma _d(\empty... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
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e7bac17e097ea7853e909b6eb50a9e1119c5b27a | subsection | 12 | 129 | Rationalizable Strategies and Aggregate Defense Effort | Henceforth, we denote the player utilities as U_d(\rho , \sigma _a) and U_a(\rho , \sigma _a), and use \sigma _d and \rho _e(\sigma _d) interchangeably in representing the defender's strategy. For the sequential game \widetilde{\Gamma }, we analogously denote the security effort vector given the strategy \widetilde{\si... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
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41a29c6aa778a116dc4b510e3e40d2506c2266ef | subsection | 13 | 129 | Rationalizable Strategies and Aggregate Defense Effort | \left(\tilde{\rho }^{*}, \widetilde{\sigma }_a^*\right) in \widetilde{\Gamma }) satisfies:
\begin{alignat*}{2}
\rho _e^{*}&=\sigma _a^*(e)=0, &&\quad \forall e\in \mathcal {E}\setminus \bar{\mathcal {E}}, \\
\tilde{\rho }^{*}_e&=\widetilde{\sigma }_a^*(e, \tilde{\rho })=0, &&\quad \forall e\in \mathcal {E}\setminus \ba... | {
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} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
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a4c1f2c84b522fd0d48027c4e3399f09aa9ffaf3 | subsection | 14 | 129 | Rationalizable Strategies and Aggregate Defense Effort | In Sec. \ref {in_regime}, we show that the space of cost parameters (p_a, p_d) \in \mathbb {R}_{>0}^2 can be partitioned into qualitatively distinct equilibrium regimes.
\subsection {Strategic Equivalence to Zero-Sum Game}
Our notion of strategic equivalence is the same as the best-response equivalence defined in \cite... | {
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} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
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5df304f68fe7b4920fab4ccd7c966b81f0d67087 | subsection | 15 | 129 | Rationalizable Strategies and Aggregate Defense Effort | \quad & V(\sigma _a)=\sum _{e\in \bar{\mathcal {E}}} \min \left\lbrace \sigma _a(e)\cdot \left( C_{\emptyset }-p_a\right)+p_d,~ \sigma _a(e) \cdot \left(C_{e}-p_a\right)\right\rbrace +\sigma _a(\emptyset ) \cdot C_{\emptyset }, \\
&\sum _{e\in \bar{\mathcal {E}}} \sigma _a(e) +\sigma _a(\emptyset )=1, \\
& \sigma _a(\e... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
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cf9b0e9e4ff35481c54e02d4f657a992fbb05414 | subsection | 16 | 129 | Rationalizable Strategies and Aggregate Defense Effort | Furthermore, given any \sigma _a and any e\in \bar{\mathcal {E}}, we can write:&\min \left\lbrace \sigma _a(e) \cdot \left(C_{\emptyset }-p_a\right)+p_d,~ \sigma _a(e) \cdot \left(C_{e}-p_a\right)\right\rbrace \\
=&
\left\lbrace
\begin{array}{ll}
\sigma _a(e) \cdot \left(C_{\emptyset }-p_a\right)+p_d& \quad \text{if $... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
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7c1ef3d09c75ba9b03a69bdccd8ac3abe56a8c3d | subsection | 17 | 129 | Rationalizable Strategies and Aggregate Defense Effort | The following lemma analyzes the defender's best response to the attacker's strategy, and shows that no facility is targeted with probability higher than the threshold probability in equilibrium.Lemma 2
Given any strategy of the attacker \sigma _a\in \Delta (S_a), for any defender's security effort \rho that is a best... | {
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} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
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32547d3d8638914583c56d5b6be218896b250ad1 | subsection | 18 | 129 | Rationalizable Strategies and Aggregate Defense Effort | Hence, the attacker would be better off by choosing the no attack action.Now, we can re-write V(\sigma _a) as defined in (REF ) as follows:V(\sigma _a)&\stackrel{(\ref {upper_bound})}{=}\sum _{e\in \lbrace \bar{\mathcal {E}}|\sigma _a(e) \le \frac{p_d}{C_{e}-C_{\emptyset }}\rbrace } \sigma _a(e) \left(C_{e}-p_a\right)+... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
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] | [
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1b03e667210074d7733d50f19ed2cf7bffe62142 | subsection | 19 | 129 | Characterization of NE in | We are now in the position to introduce the equilibrium regimes. Each regime corresponds to a range of cost parameters such that the qualitative properties of equilibrium (i.e. the set of facilities that are targeted and secured) do not change in the interior of each regime.We say that a facility e is vulnerable if C_{... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
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78f5e3fd0d022d137b6457e0f6610ed42942f612 | subsection | 20 | 129 | Characterization of NE in | We formally define these 2K+1 regimes as follows:Type I regimes \Lambda ^i, i=0, \dots , K:
If i=0:
p_a> C_{(1)}-C_{\emptyset }, \text{ and }p_d>0
If i=1, \dots , K-1:
C_{(i+1)}-C_{\emptyset }< p_a< C_{(i)}-C_{\emptyset }, \text{ and } 0<p_d< \left(\sum _{k=1}^{i} \frac{E_{(k)}}{C_{(k)}-C_{\emptyset }}\right)^{-1}... | {
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} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
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ff9f5f103c96b3a96922b0cd6f63661a7568e8d4 | subsection | 21 | 129 | Characterization of NE in | If i=1, \dots , K,
\rho _e^{*}&=\frac{C_{(k)}-p_a-C_{\emptyset }}{C_{(k)}-C_{\emptyset }},&& \quad \forall e\in \bar{\mathcal {E}}_{(k)}, \quad \forall k=1, \dots , i \\
\rho _e^{*}&=0, &&\quad \forall e\in \mathcal {E}\setminus \left(\cup _{k=1}^{i} \bar{\mathcal {E}}_{(k)}\right)\\
\sigma _a^*(e)&= \frac{p_d}{C_{(k)... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
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bf748d25b328b47630951622fe78de49c4798882 | subsection | 22 | 129 | Characterization of NE in | Also recall that the costs \lbrace C_{(k)}\rbrace _{k=1}^K are ordered according to (). Thus, in equilibrium, the attacker targets the facilities in \bar{\mathcal {E}}_{(k)} with the threshold attack probability starting from k=1 and proceeding to k=2, 3, \dots K until either all the vulnerable facilities are targeted ... | {
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} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
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0.04120364785194397,
0.01646619848906994,
0.019960878416895866,
0.022234709933400154,
-0.034214287996292114,
0.014543361961841583,
-0.029742930084466934,
... | |
a9e3c79cd711144ad547655bd50435ff0ab480b4 | subsection | 23 | 129 | Sequential game | In this section, we characterize the set of SPE in the game \widetilde{\Gamma } for any given attack and defense cost parameters. The sequential game \widetilde{\Gamma } is no longer strategically equivalent to a zero-sum game. Hence, the proof technique we used for equilibrium characterization in game \Gamma does not ... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
-0.03240496665239334,
0.000648881250526756,
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0.02135920524597168,
-0.004710467532277107,
0.024639369919896126,
-0.034327294677495956,
-... | |
be1931ec0ad03fcc6f25fd5aa2d80ca7410fac68 | subsection | 24 | 129 | Properties of SPE | By definition of SPE, for any security effort vector \tilde{\rho }\in [0, 1]^{|\mathcal {E}|} chosen by the defender in the first stage, the attacker's equilibrium strategy in the second stage is a best response to \tilde{\rho }, i.e. \widetilde{\sigma }_a^*(\tilde{\rho }) satisfies (). As we describe next, the propert... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
0.01702502742409706,
0.011616988107562065,
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0.032768599689006805,
0.003632692387327552,
0.04164724424481392,
-0.03423311933875084,
-0.02398... | |
6bdf2fa4180b4a74125cc0836fa12288431c1df2 | subsection | 25 | 129 | Properties of SPE | In particular, no attack action is not chosen in attacker's best response.Now recall that any SPE (\tilde{\rho }^{*}, \widetilde{\sigma }_a^*(\tilde{\rho }^{*})) must satisfy both (REF ) and (). Thus, for an equilibrium security effort \tilde{\rho }^{*}, an attacker's best response \widetilde{\sigma }_a(\tilde{\rho }^{... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
0.013429829850792885,
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0.030949654057621956,
0.03131592273712158,
0.010675189085304737,
0.021853996440768242,
-0.0403810553252697,
-0.030... | |
0a24a8e13838b7e6fa0bd6d65b6911bd58f041f0 | subsection | 26 | 129 | Properties of SPE | In this case, by applying Lemma REF , we know that \widetilde{\sigma }_a^*(\tilde{\rho }^{*}) \in BR(\tilde{\rho }^{*}) = \Delta (\bar{\mathcal {E}}^{\diamond }), where \bar{\mathcal {E}}^{\diamond } is defined in (REF ). Hence, the total attack probability is 1.Case 2: For any e\in \lbrace \bar{\mathcal {E}}|C_{e}-p_a... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
0.011466900818049908,
0.02738933637738228,
-0.026290711015462875,
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0.013328460045158863,
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0.03250099718570709,
0.037139635533094406,
0.037414293736219406,
0.0360715277493,
-0.007430979050695896,
0.044006042182445526,
-0.03912326321005821,
-0.0130... | |
91b860d1dd3ae9fcf491c044eb5ddf69ffaa5055 | subsection | 27 | 129 | Properties of SPE | As we describe next, the properties of SPE crucially depend on a threshold security effort level defined as follows:\widehat{\rho }_e\stackrel{\Delta }{=}\frac{C_{e}-p_a-C_{\emptyset }}{C_{e}-C_{\emptyset }}, \quad \forall e\in \bar{\mathcal {E}}.The following lemma presents the best response correspondence BR(\tilde{\... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
0.0124736363068223,
0.010413769632577896,
-0.04690392315387726,
-0.010421399027109146,
-0.01034510787576437,
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0.03997666761279106,
0.02429116703569889,
0.03274424746632576,
0.03481937199831009,
-0.012130324728786945,
0.043760720640420914,
-0.031111614778637886,
-0.0169... | |
37fb48de2fa5b3db672d4e22c17e7e46c99d7cf8 | subsection | 28 | 129 | Properties of SPE | The next lemma shows that depending on whether the defender secures each vulnerable facility e with the threshold effort \widehat{\rho }_e or not, the total attack probability in equilibrium is either 0 or 1. Thus, the defender being the first mover determines
whether the attacker is fully deterred from conducting an a... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
0.002819883404299617,
0.020483268424868584,
-0.030877534300088882,
0.009692156687378883,
0.0053116073831915855,
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0.03455597534775734,
0.03449492156505585,
0.026893828064203262,
0.01819378137588501,
-0.010424792766571045,
0.018239570781588554,
-0.045148663222789764,
-0.... | |
7c92629b4c78ecbf6b915ad0a76aefb5156a7dad | subsection | 29 | 129 | Properties of SPE | Hence, Lemma REF shows that the total attack probability is 0.Case 3: For any e\in \lbrace \bar{\mathcal {E}}|C_{e}-p_a>C_{\emptyset }\rbrace , \tilde{\rho }^{*}_e\ge \widehat{\rho }_e, and the set \bar{\mathcal {E}}^{*} in (REF ) is non-empty. Again from Lemma REF , we know that \widetilde{\sigma }_a^*(\tilde{\rho }^{... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
0.00719989649951458,
0.02857065573334694,
-0.010622423142194748,
0.012163895182311535,
0.014766084030270576,
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0.03012738935649395,
0.039101507514715195,
0.03003581613302231,
0.012400457635521889,
-0.018543453887104988,
0.046457838267087936,
-0.04340541735291481,
-0.021... | |
3d0ab06441fd60ae7ad2b7e11d440f96e46aa363 | subsection | 30 | 129 | Characterization of SPE | Recall that in Sec. , type I and type II regimes for the game \Gamma can be distinguished based on a threshold defense cost \bar{p}_d(p_a). It turns out that in \widetilde{\Gamma }, there are still 2 K+1 regimes. Again, each regime denotes distinct ranges of cost parameters, and can be categorized either as type \widet... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
-0.04152930900454521,
0.015493392013013363,
-0.062461789697408676,
-0.018628686666488647,
-0.01611129753291607,
-0.021191848441958427,
0.04094954580068588,
0.04860851541161537,
0.025646865367889404,
0.012495409697294235,
-0.03399239480495453,
0.008505727164447308,
-0.039637453854084015,
-0... | |
2dc00683e400bba7650e02b9df69242de6c46f05 | subsection | 31 | 129 | Characterization of SPE | \end{array}
\right.For any i=1, \dots , K, and any attack cost C_{(i+1)}-C_{\emptyset }\le p_a< C_{(i)}-C_{\emptyset }, but 0<p_a<C_{(K)}-C_{\emptyset } if i=K, the threshold \widetilde{p}_d(p_a) is defined as follows:\widetilde{p}_d(p_a)=\left\lbrace
\begin{array}{ll}
p_d^{ij}(p_a), & \quad \text{if $\frac{\sum _{k=j... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
-0.02271728776395321,
0.024792203679680824,
-0.09300509095191956,
-0.001741175539791584,
-0.02021518163383007,
-0.03228326514363289,
0.08043354004621506,
0.030528739094734192,
0.014333708211779594,
0.006514628417789936,
-0.018720021471381187,
-0.0019280706765130162,
-0.02473117783665657,
-... | |
c7c1b55f1e00f97aa80deff461b88b319a44ad80 | subsection | 32 | 129 | Characterization of SPE | If i=K:
0<p_a< C_{(K)}-C_{\emptyset }, \text{ and } \quad 0<p_d< \widetilde{p}_d(p_a).
Type \widetilde{\mathrm {II}} regimes \widetilde{\Lambda }_j, j=1, \dots , K:
If j=1:
0< p_a< \widetilde{p}_d^{-1}(p_d), \text{ and } \quad p_d> \left(\frac{E_{(1)}}{C_{(1)}-C_{\emptyset }}\right)^{-1}
If j=2, \dots , K:
0< ... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
-0.028722839429974556,
0.023457493633031845,
-0.04718970134854317,
-0.004933399613946676,
-0.009164753369987011,
-0.0348275862634182,
0.05204297602176666,
0.03754420205950737,
0.002943633124232292,
0.021885521709918976,
-0.017932698130607605,
-0.010011786594986916,
-0.036781106144189835,
-... | |
cdd5542a5f5377a626e277bf20c2d6efa1381045 | subsection | 33 | 129 | Characterization of SPE | If i=1, \dots , K,
\tilde{\rho }^{*}_e&=\frac{C_{(k)}-p_a-C_{\emptyset }}{C_{(k)}-C_{\emptyset }}, && \quad \forall e\in \bar{\mathcal {E}}_{(k)}, \quad \forall k=1, \dots , i, \\
\tilde{\rho }^{*}_e&=0, &&\quad \forall e\in \mathcal {E}\setminus \left(\cup _{k=1}^{i} \bar{\mathcal {E}}_{(k)}\right),\\
\widetilde{\sig... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
0.000514898682013154,
0.03399094194173813,
-0.028635995462536812,
-0.011579499579966068,
-0.011632896028459072,
-0.04058164358139038,
0.04406007006764412,
0.06407628208398819,
0.012319427914917469,
0.028102025389671326,
-0.0037110846024006605,
-0.011800714768469334,
0.00030703216907568276,
... | |
295a47dfc1b0bc59c2bb683427075e006ee19e01 | subsection | 34 | 129 | Characterization of SPE | If j=2, \dots , K,
\tilde{\rho }^{*}_e&=\frac{C_{(k)}-C_{(j)}}{C_{(k)}-C_{\emptyset }}, &&\quad \forall e\in \bar{\mathcal {E}}_{(k)},\quad \forall k=1, \dots , j-1,\\
\tilde{\rho }^{*}_e&=0, &&\quad \forall e\in \mathcal {E}\setminus \left(\cup _{k=1}^{j-1} \bar{\mathcal {E}}_{(k)}\right),\\
\widetilde{\sigma }_a^*(\... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
-0.015221555717289448,
0.04068237170577049,
-0.045351844280958176,
-0.0008087643655017018,
-0.00613440154120326,
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0.03393758460879326,
0.036531735211610794,
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0.031648628413677216,
-0.006302257999777794,
0.019242487847805023,
-0.03537199646234512,
-... | |
d58ec568940e1dad257dde105e7e4569200f81bc | subsection | 35 | 129 | Characterization of SPE | Again, each regime denotes distinct ranges of cost parameters, and can be categorized either as type \widetilde{\mathrm {I}} or type \widetilde{\mathrm {II}}. However, in contrast to \Gamma , the regime boundaries in this case are more complicated; in particular, they are non-linear in the cost parameters p_a and p_d.T... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
-0.026523984968662262,
0.020190583541989326,
-0.06501276046037674,
-0.02428058721125126,
-0.013139902614057064,
-0.009522995911538601,
0.04499005153775215,
0.0366269089281559,
0.04215146601200104,
0.036108024418354034,
-0.035192351788282394,
0.008302099071443081,
-0.007497069891542196,
-0.... | |
cc4d37580c293914e46a21155c2592a820afce0b | subsection | 36 | 129 | Characterization of SPE | \end{array}
\right.Lemma 5
Given any attack cost 0\le p_a<C_{(1)}-C_{\emptyset }, the threshold \widetilde{p}_d(p_a) is a strictly increasing and continuous function of p_a.Furthermore, for any 0<p_a<C_{(1)}-C_{\emptyset }, \widetilde{p}_d(p_a)>\bar{p}_d(p_a). If p_a=0, \widetilde{p}_d(0)=\bar{p_d}(0). If p_a\rightarr... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
-0.05005601420998573,
0.024036044254899025,
-0.07282539457082748,
0.003840044140815735,
-0.007626675069332123,
-0.03323841467499733,
0.09388554841279984,
0.05130741745233536,
0.016817599534988403,
0.005612225737422705,
-0.037511490285396576,
0.0036874343641102314,
-0.027393460273742676,
-0... | |
61fedd5b28bc874f7bfc46a31f15d14e2508af4b | subsection | 37 | 129 | Characterization of SPE | We now provide full characterization of SPE in each regime.Theorem 2
The defender's equilibrium security effort vector \tilde{\rho }^{*}=\left(\tilde{\rho }^{*}_e\right)_{e\in \mathcal {E}} is unique in each regime. Specifically, SPE in each regime is as follows:Type \widetilde{\mathrm {I}} regimes \widetilde{\Lambda ... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
-0.02097923681139946,
0.0056910947896540165,
-0.019911203533411026,
-0.010611679404973984,
-0.014677836559712887,
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0.020506249740719795,
0.038632310926914215,
0.026502497494220734,
0.03371935710310936,
-0.00890282541513443,
0.0012377749662846327,
-0.040493741631507874,
... | |
3e5bdaf917d90ee9b03886214863eb8efd54ccc9 | subsection | 38 | 129 | Characterization of SPE | If j=2, \dots , K,
\tilde{\rho }^{*}_e&=\frac{C_{(k)}-C_{(j)}}{C_{(k)}-C_{\emptyset }}, &&\quad \forall e\in \bar{\mathcal {E}}_{(k)},\quad \forall k=1, \dots , j-1,\\
\tilde{\rho }^{*}_e&=0, &&\quad \forall e\in \mathcal {E}\setminus \left(\cup _{k=1}^{j-1} \bar{\mathcal {E}}_{(k)}\right),\\
\widetilde{\sigma }_a^*(\... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
-0.013845046982169151,
0.038201648741960526,
-0.03682858869433403,
0.0048972563818097115,
-0.004439568612724543,
-0.017880326136946678,
0.027461251243948936,
0.029719175770878792,
-0.00011174011160619557,
0.03652346134185791,
-0.0018021445721387863,
0.01733110100030899,
-0.03475373610854149,... | |
189cef42fdf0fe9e23dd5e8122ec33c5c2b5c26e | subsection | 39 | 129 | Comparison of | Sec. REF deals with the comparison of players' equilibrium utilities in the two games. In Sec. REF , we compare the equilibrium regimes and discuss the distinctions in equilibrium properties of the two games. This leads us to an understanding of the effect of timing of play, i.e. we can identify situations in which the... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
-0.037878770381212234,
0.0010101132793352008,
-0.03522329032421112,
0.021976402029395103,
-0.048256516456604004,
-0.0046814316883683205,
0.0312553271651268,
0.04434959962964058,
0.050057362765073776,
0.003229691879823804,
-0.005341486539691687,
0.011705487035214901,
-0.04963004216551781,
-... | |
6abe718e3266f98ad4222c38088c6bb0dd999d08 | subsection | 40 | 129 | Comparison of Equilibrium Utilities | The equilibrium utilities in both games are unique, and can be directly derived using Theorems REF and REF . We denote the equilibrium utilities of the defender and attacker in regime \Lambda ^i (resp. \Lambda _j) as U_d^{\Lambda ^i} and U_a^{\Lambda ^i} (resp. U_d^{\Lambda _j} and U_a^{\Lambda _j}) in \Gamma , and \wi... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
-0.03887476399540901,
0.033046603202819824,
-0.05208730325102806,
-0.042750034481287,
-0.024273842573165894,
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0.04516063630580902,
0.04842562973499298,
0.04311620444059372,
0.00041384538053534925,
-0.0346333272755146,
0.011290159076452255,
-0.04455035924911499,
-0.0306... | |
c5fad0800b3f811e8c92233fa76a253ab09261e6 | subsection | 41 | 129 | Comparison of Equilibrium Utilities | If j=2, \dots , K:
U_d^{\Lambda _j}&=\widetilde{U}_d^{\widetilde{\Lambda }_j}=-C_{(j)}-\sum _{k=1}^{j-1} \frac{\left(C_{(k)}-C_{(j)}\right) p_dE_{(k)}}{C_{(k)}-C_{\emptyset }} , \text{ and } \quad U_a^{\Lambda _j}=\widetilde{U}_a^{\widetilde{\Lambda }_j}=C_{(j)}-p_a.\\From our results so far, we can summarize the simi... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
-0.018462520092725754,
0.05160350725054741,
-0.07031016051769257,
-0.020156189799308777,
-0.04080064594745636,
-0.042509570717811584,
0.032530657947063446,
0.03268323838710785,
0.016265328973531723,
0.016295844689011574,
-0.012054042890667915,
0.012855102308094501,
-0.03546024486422539,
-0... | |
eb220778ae67251b1bebf16ae5a655b92574321e | subsection | 42 | 129 | Comparison of Equilibrium Utilities | Specifically,Type I (\widetilde{\mathrm {I}}) regimes \Lambda ^i (\widetilde{\Lambda }^i):
If i=0:
U_d^{\Lambda _0}&=\widetilde{U}_d^{\widetilde{\Lambda }^{0}}=-C_{\emptyset }, \text{ and } \quad U_a^{\Lambda _0}= \widetilde{U}_a^{\widetilde{\Lambda }^0}=C_{\emptyset }.\\
If i=1, \dots , K:
U_d^{\Lambda ^i}&=-C_{\... | {
"cite_spans": []
} | 1804.00391 | Securing Infrastructure Facilities: When does proactive defense help? | [
"Manxi Wu",
"Saurabh Amin"
] | [
"cs.GT"
] | 2,018 | en | Computer Science | [
-0.03161374852061272,
0.03896791487932205,
-0.08300135284662247,
-0.02058250457048416,
-0.02952345833182335,
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0.03948667272925377,
0.017866650596261024,
0.010764237493276596,
-0.0069078789092600346,
0.00013839121675118804,
-0.0342685729265213,
-0.0... |
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