HyperPCTL: A Temporal Logic for Probabilistic Hyperproperties

Ábrahám, Erika; Bonakdarpour, Borzoo

doi:10.1007/978-3-319-99154-2_2

Cited by 41 publications

(50 citation statements)

References 19 publications

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“…Our framework is based on an underlying standard automata model for formal languages, augmented with quantified word variables that are assigned words from a set of words in the hyperlanguage. This formalism is in line with logics for hyperproperties (e.g., HyperLTL [13] and HyperPCTL [2,1]). These logics express the behavior of infinite trace systems.…”

Section: Introductionmentioning

confidence: 85%

Finite-Word Hyperlanguages

Bonakdarpour

Sheinvald

2021

Language and Automata Theory and Applications

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Formal languages are in the core of models of computation and their behavior. A rich family of models for many classes of languages have been widely studied. Hyperproperties lift conventional trace-based languages from a set of execution traces to a set of sets of executions. Hyperproperties have been shown to be a powerful formalism for expressing and reasoning about information-flow security policies and important properties of cyber-physical systems. Although there is an extensive body of work on formal-language representation of trace properties, we currently lack such a general characterization for hyperproperties.We introduce hyperlanguages over finite words and models for expressing them. Essentially, these models express multiple words by using assignments to quantified word variables. Relying on the standard models for regular languages, we propose hyperregular expressions and finite-word hyperautomata (NFH), for modeling the class of regular hyperlanguages. We demonstrate the ability of regular hyperlanguages to express hyperproperties for finite traces. We explore the closure properties and the complexity of the fundamental decision problems such as nonemptiness, universality, membership, and containment for various fragments of NFH.

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Section: Introductionmentioning

confidence: 85%

Finite-Word Hyperlanguages

Bonakdarpour

Sheinvald

2021

Language and Automata Theory and Applications

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“…It is also possible to extend hyperlogics in other quantitative dimensions orthogonal to time. Hyper-PCTL [41] can express probabilisitic hyperproperties, e.g., the probability distribution of the low-security outputs is independent of the high-security inputs. In [42], specialised algorithms are developed for verifying quantitative hyperproperties, e.g., there is a bound on the number of traces with the same low-security inputs but different low-level outputs.…”

Section: Related Workmentioning

confidence: 99%

Timed hyperproperties

Zhou

Jones

2021

Information and Computation

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“…Finally, for the first two rules of (2), we assume that Π is contained in fv(φ) or fv(p) for the probability quantification to be non-trivial. Observe that HyperPSTL can be viewed as the probabilistic version of HyperSTL [23] by replacing the existential and universal quantifiers over signals with probabilistic quantifiers over paths in (2).…”

Section: Syntaxmentioning

confidence: 99%

“…Another new feature of HyperPSTL is the arithmetics and comparisons of the probabilities of multiple sub-properties. For example, we can compare the satisfaction probability of φ 1 and φ 2 by the HyperPSTL formula p 1 < p 2 , where p 1 = P Π 1 φ 1 and p 2 = P Π 2 φ 2 , according to the syntax (1), (2). For simplicity, let Π 1 = fv(φ 1 ) and Π 2 = fv(φ 2 ).…”

Section: Smc Of Joint Probabilitiesmentioning

confidence: 99%

“…Conventional probabilistic temporal logics, such as the probabilistic computational tree logic (PCTL) [15], as well as its extension PCTL * [3], can only specify probabilistic properties without explicitly quantifying over different paths of the system; that is, they cannot simultaneously and explicitly quantify over multiple distinctive paths to fully express their inter-relations. This prevents them from capturing important safety/performance hyperproperties [2,7] that involve multiple execution paths, such as sensitivity to model errors, detectability of system anomalies, and fairness when more than once process/client are controlled/serviced. For example, consider embedded controllers such as the Toyota Powertrain control system benchmark [19], for which both exhaustive (e.g., [11]) and statistical (e.g., [24]) verification techniques have been introduced.…”

Section: Introductionmentioning

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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HyperPCTL: A Temporal Logic for Probabilistic Hyperproperties

Cited by 41 publications

References 19 publications

Finite-Word Hyperlanguages

Finite-Word Hyperlanguages

Timed hyperproperties

Statistical Verification of Hyperproperties for Cyber-Physical Systems

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