Statistical Model Checking for Cyber-Physical Systems

Clarke, Edmund M.; Zuliani, Paolo

doi:10.1007/978-3-642-24372-1_1

Cited by 134 publications

(117 citation statements)

References 23 publications

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“…More recently, an estimation approach [2] has been taken in which the goal is to estimate the probability that a system property holds. SMC has been applied to a wide variety of systems, such as stochastic hybrid automata [4], and real time systems [5].…”

Section: Related Workmentioning

confidence: 99%

“…Approaches proposed to finding the importance sampling bias function include Cross-Entropy Method [2,9] and Coupling [1].…”

Section: Related Workmentioning

confidence: 99%

“…The actual input distribution f is uniform in the range [0,10], and x Φ = [2.99, 3.01] ∪ [6.99, 7.01]. Figure 1(b) shows a tilted distribution g uniform in the range [2,10]. While g makes Φ more likely than f , it still assigns positive weight to large parts -e.g., (3.01, 6.99) -of the input space that do not belong to x Φ .…”

Section: Introductionmentioning

confidence: 99%

“…It is known [2] that for Bernoulli trials, relative error is related to the number of trials N and the probability of the event p as:…”

Section: Introductionmentioning

confidence: 99%

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Semantic Importance Sampling for Statistical Model Checking

Hansen¹,

Wrage²,

Chaki³

et al. 2015

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Abstract. Statistical Model Checking (SMC) is a technique, based onMonte-Carlo simulations, for computing the bounded probability that a specific event occurs during a stochastic system's execution. Estimating the probability of a "rare" event accurately with SMC requires many simulations. To this end, Importance Sampling (IS) is used to reduce the simulation effort. Commonly, IS involves "tilting" the parameters of the original input distribution, which is ineffective if the set of inputs causing the event (i.e., input-event region) is disjoint. In this paper, we propose a technique called Semantic Importance Sampling (SIS) to address this challenge. Using an SMT solver, SIS recursively constructs an abstract indicator function that over-approximates the input-event region, and then uses this abstract indicator function to perform SMC with IS. By using abstraction and SMT solving, SIS thus exposes a new connection between the verification of non-deterministic and stochastic systems. We also propose two optimizations that reduce the SMT solving cost of SIS significantly. Finally, we implement SIS and validate it on several problems. Our results indicate that SIS reduces simulation effort by multiple orders of magnitude even in systems with disjoint input-event regions.

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Section: Related Workmentioning

confidence: 99%

“…Approaches proposed to finding the importance sampling bias function include Cross-Entropy Method [2,9] and Coupling [1].…”

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…It is known [2] that for Bernoulli trials, relative error is related to the number of trials N and the probability of the event p as:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Semantic Importance Sampling for Statistical Model Checking

Hansen¹,

Wrage²,

Chaki³

et al. 2015

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“…The paper [10] employs statistical model checking for verifying unbounded temporal properties. The paper [9] has discussed the use of importance sampling to address the issue of rare events in statistical verification of cyber-physical systems. A distributed implementation of statistical model checking is proposed in [7] and a set-oriented method for statistical verification of dynamical systems is presented in [31].…”

Section: Introductionmentioning

confidence: 99%

Multilevel Monte Carlo Method for Statistical Model Checking of Hybrid Systems

Soudjani

Majumdar

Nagapetyan

2017

Quantitative Evaluation of Systems

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Abstract. We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo method (MLMC) and work on a sequence of discrete-time stochastic processes whose executions approximate and converge weakly to that of the original continuous-time stochastic hybrid system with respect to satisfaction of the property of interest. With focus on bounded-horizon reachability, we recast the model checking problem as the computation of the distribution of the exit time, which is in turn formulated as the expectation of an indicator function. This latter computation involves estimating discontinuous functionals, which reduces the bound on the convergence rate of the Monte Carlo algorithm. We propose a smoothing step with tunable precision and formally quantify the error of the MLMC approach in the mean-square sense, which is composed of smoothing error, bias, and variance. We formulate a general adaptive algorithm which balances these error terms. Finally, we describe an application of our technique to verify a model of thermostatically controlled loads.

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Statistical Model Checking the 2018 Edition!

Larsen

Legay

2018

Leveraging Applications of Formal Methods, Verification and Validation. Verification

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Statistical Model Checking for Cyber-Physical Systems

Cited by 134 publications

References 23 publications

Semantic Importance Sampling for Statistical Model Checking

Semantic Importance Sampling for Statistical Model Checking

Multilevel Monte Carlo Method for Statistical Model Checking of Hybrid Systems

Statistical Model Checking the 2018 Edition!

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