Revisiting MITL to Fix Decision Procedures

Roohi, Nima; Viswanathan, Mahesh

doi:10.1007/978-3-319-73721-8_22

Cited by 6 publications

(5 citation statements)

References 13 publications

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“…The statistical model checking algorithm examines the correctness of φ on each sample signals σ i . This process can be performed automatically by existing model checking algorithms from [29], [32]. With a slight abuse of notation, we represent "True" and "False" by 1 and 0 and define the truth values by…”

Section: Sequential Probability Ratio Testmentioning

confidence: 99%

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Differentially Private Algorithms for Statistical Verification of Cyber-Physical Systems

Wang

Sibai

Mitra

et al. 2022

IEEE Open J. Control. Syst.

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Statistical model checking is a class of sequential algorithms that can verify specifications of interest on an ensemble of cyber-physical systems (e.g., whether 99% of cars from a batch meet a requirement on their energy efficiency). These algorithms infer the probability that given specifications are satisfied by the systems with provable statistical guarantees by drawing sufficient numbers of independent and identically distributed samples. During the process of statistical model checking, the values of the samples (e.g., a user's car energy efficiency) may be inferred by intruders, causing privacy concerns in consumer-level applications (e.g., automobiles and medical devices). This paper addresses the privacy of statistical model checking algorithms from the point of view of differential privacy. These algorithms are sequential, drawing samples until a condition on their values is met. We show that revealing the number of samples drawn can violate privacy. We also show that the standard exponential mechanism that randomizes the output of an algorithm to achieve differential privacy fails to do so in the context of sequential algorithms. Instead, we relax the conservative requirement in differential privacy that the sensitivity of the output of the algorithm should be bounded to any perturbation for any data set. We propose a new notion of differential privacy which we call expected differential privacy (EDP). Then, we propose a novel expected sensitivity analysis for the sequential algorithm and propose a corresponding exponential mechanism that randomizes the termination time to achieve the EDP. We apply the proposed exponential mechanism to statistical model checking algorithms to preserve the privacy of the samples they draw. The utility of the proposed algorithm is demonstrated in a case study.

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Section: Sequential Probability Ratio Testmentioning

confidence: 99%

“…Thus, by taking the ratios of ( 31) and (32) and applying (29) and (30) results in that for any k ∈ N, we can derive (28).…”

Section: Proofmentioning

confidence: 99%

Differentially Private Algorithms for Statistical Verification of Cyber-Physical Systems

Wang

Sibai

Mitra

et al. 2022

IEEE Open J. Control. Syst.

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“…is is because it has recently been shown that the common semantics of MITL cannot ensure that the formulas ¬(φU I ψ ) and (¬φ)R I (¬ψ ) are equivalent for the continuous-time domain (see [21] for details). Following the semantics of MITL, the satis ability/model checking problems for MITL with abstract atomic propositions are known to be EXPSPACE-complete [20,21]. e corresponding decision procedure has a close connection with timed automata.…”

Section: De Nition 23 (Mitl Semantics)mentioning

confidence: 99%

Verifying Stochastic Hybrid Systems with Temporal Logic Specifications via Model Reduction

Wang¹,

Roohi²,

West³

et al. 2020

Preprint

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We present a scalable methodology to verify stochastic hybrid systems. Using the Mori-Zwanzig reduction method, we construct a nite state Markov chain reduction of a given stochastic hybrid system and prove that this reduced Markov chain is approximately equivalent to the original system in a distributional sense. Approximate equivalence of the stochastic hybrid system and its Markov chain reduction means that analyzing the Markov chain with respect to a suitably strengthened property, allows us to conclude whether the original stochastic hybrid system meets its temporal logic speci cations. We present the rst statistical model checking algorithms to verify stochastic hybrid systems against correctness properties, expressed in the linear inequality linear temporal logic (iLTL) or the metric interval temporal logic (MITL).CCS Concepts: •Computer systems organization → Embedded and cyber-physical systems; •Security and privacy → Formal methods and theory of security; • eory of computation → Abstraction;

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“…always ϕ within I) operators are respectively defined to be ⊤U I φ and ⊥R I φ. Note that allowing negation only in front of atomic propositions, which is called negated normal form is not a restriction, and in general every formula that is not in negated normal form can be converted to an equivalent one that is in negated normal form [1,9,10,19]. Therefore, for any STL formula φ, we use ¬φ to denote a STL formula in negated normal form that is equivalent with negation of φ.…”

Section: Signal Temporal Logicmentioning

confidence: 99%

“…Semantics of a STL formula can be defined on both continuous and discrete time domains. While continuous semantics are usually what one uses for specifying desired behavior of a cyberphysical system, directly verifying them is often computationally very expensive if not undecidable [1,9,17,19]. One the other hand, discrete semantics are usually easier to verify.…”

Section: Signal Temporal Logicmentioning

confidence: 99%

Parameter Invariant Monitoring for Signal Temporal Logic

Roohi

Kaur

Weimer

et al. 2018

Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (Part of CPS Week)

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Signal Temporal Logic (STL) is a prominent specification formalism for real-time systems, and monitoring these specifications, specially when (for different reasons such as learning) behavior of systems can change over time, is quite important. There are three main challenges in this area: (1) full observation of system state is not possible due to noise or nuisance parameters, (2) the whole execution is not available during the monitoring, and (3) computational complexity of monitoring continuous time signals is very high. Although, each of these challenges has been addressed by different works, to the best of our knowledge, no one has addressed them all together. In this paper, we show how to extend any parameter invariant test procedure for single points in time to a parameter invariant test procedure for efficiently monitoring continuous time executions of a system against STL properties. We also show, how to extend probabilistic error guarantee of the input test procedure to a probabilistic error guarantee for the constructed test procedure.

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Revisiting MITL to Fix Decision Procedures

Cited by 6 publications

References 13 publications

Differentially Private Algorithms for Statistical Verification of Cyber-Physical Systems

Differentially Private Algorithms for Statistical Verification of Cyber-Physical Systems

Verifying Stochastic Hybrid Systems with Temporal Logic Specifications via Model Reduction

Parameter Invariant Monitoring for Signal Temporal Logic

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