Statistical Model Checking for Hyperproperties

Wang, Yu; Nalluri, Siddhartha; Bonakdarpour, Borzoo; Pajić, Miroslav

doi:10.48550/arxiv.1902.04111

Cited by 2 publications

(4 citation statements)

References 20 publications

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“…To simplify our presentation of the HyperPSTL syntax and semantics, while considering SMC of specific hyperproperties of complex CPS, in the proposed HyperPSTL, we have disallowed nested existential and universal quantifies on states to avoid exhaustive iteration on the possibly infinite state space. Still, this logic can be augmented (as done in detail in [31]) by allowing nested existential and universal quantifications over multiple states.…”

Section: Discussionmentioning

confidence: 99%

“…Finally, note that to simplify our presentation of HyperPSTL syntax and semantics, while allowing for verification of complex systems such as P 2 HIOA, we only include simultaneous or consecutive probabilistic quantification (e.g., P {π 1 , π 2 } or P π 1 P π 2 ) over the paths from a single initial state. HyperPSTL can be augmented by allowing nested existential and universal quantification over multiple states in the same way as [2,31]. Specifically, in addition to the probabilistic quantification over the paths, one can add extra state quantification of these paths to specify from which state the path starts, like ∃X π 1 1 .∀X π 2 2 .P {π 1 , π 2 } .…”

Section: Syntaxmentioning

confidence: 99%

“…However, verifying such formulas generally requires exhaustive iteration over all the states, which is challenging, if not impossible, on systems with infinite state spaces like P 2 HIOA. Therefore, in this paper, we do not include state quantification which in our logic can be done as presented in [2,31].…”

Section: Syntaxmentioning

confidence: 99%

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Statistical Verification of Hyperproperties for Cyber-Physical Systems

Wang

Zarei

Bonakdarpour

et al. 2019

ACM Trans. Embed. Comput. Syst.

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Many important properties of cyber-physical systems (CPS) are defined upon the relationship between multiple executions simultaneously in continuous time. Examples include probabilistic fairness and sensitivity to modeling errors (i.e., parameters changes) for real-valued signals. These requirements can only be specified by hyperproperties. In this article, we focus on verifying probabilistic hyperproperties for CPS. To cover a wide range of modeling formalisms, we first propose a general model of probabilistic uncertain systems (PUSs) that unify commonly studied CPS models such as continuous-time Markov chains (CTMCs) and probabilistically parametrized Hybrid I/O Automata (P 2 HIOA). To formally specify hyperproperties, we propose a new temporal logic, hyper probabilistic signal temporal logic (HyperPSTL) that serves as a hyper and probabilistic version of the conventional signal temporal logic (STL). Considering the complexity of real-world systems that can be captured as PUSs, we adopt a statistical model checking (SMC) approach for their verification. We develop a new SMC technique based on the direct computation of significance levels of statistical assertions for HyperPSTL specifications, which requires no a priori knowledge on the indifference margin. Then, we introduce SMC algorithms for HyperPSTL specifications on the joint probabilistic distribution of multiple paths, as well as specifications with nested probabilistic operators quantifying different paths, which cannot be handled by existing SMC algorithms. Finally, we show the effectiveness of our SMC algorithms on CPS benchmarks with varying levels of complexity, including the Toyota Powertrain Control System.

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Section: Discussionmentioning

confidence: 99%

Section: Syntaxmentioning

confidence: 99%

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Statistical Verification of Hyperproperties for Cyber-Physical Systems

Wang

Zarei

Bonakdarpour

et al. 2019

ACM Trans. Embed. Comput. Syst.

Self Cite

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“…There is a large body of work on verifying hyperproperties. While the bulk of this literature is in a deterministic setting, there is a growing number of logics and model-checking algorithms from probabilistic hyperproperties [Ábrahám and Bonakdarpour 2018;Dimitrova et al 2020;Wang et al 2019]. To our best knowledge, these algorithms do not perform parametrized verification, and cannot prove accuracy for all possible values of .…”

Section: Related Workmentioning

confidence: 99%

Deciding accuracy of differential privacy schemes

Barthe

Chadha

Krogmeier

et al. 2021

Proc. ACM Program. Lang.

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Differential privacy is a mathematical framework for developing statistical computations with provable guarantees of privacy and accuracy. In contrast to the privacy component of differential privacy, which has a clear mathematical and intuitive meaning, the accuracy component of differential privacy does not have a generally accepted definition; accuracy claims of differential privacy algorithms vary from algorithm to algorithm and are not instantiations of a general definition. We identify program discontinuity as a common theme in existing ad hoc definitions and introduce an alternative notion of accuracy parametrized by, what we call, — the of an input x w.r.t. a deterministic computation f and a distance d , is the minimal distance d ( x , y ) over all y such that f ( y )≠ f ( x ). We show that our notion of accuracy subsumes the definition used in theoretical computer science, and captures known accuracy claims for differential privacy algorithms. In fact, our general notion of accuracy helps us prove better claims in some cases. Next, we study the decidability of accuracy. We first show that accuracy is in general undecidable. Then, we define a non-trivial class of probabilistic computations for which accuracy is decidable (unconditionally, or assuming Schanuel’s conjecture). We implement our decision procedure and experimentally evaluate the effectiveness of our approach for generating proofs or counterexamples of accuracy for common algorithms from the literature.

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Statistical Model Checking for Hyperproperties

Cited by 2 publications

References 20 publications

Statistical Verification of Hyperproperties for Cyber-Physical Systems

Statistical Verification of Hyperproperties for Cyber-Physical Systems

Deciding accuracy of differential privacy schemes

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