Rare-event verification for stochastic hybrid systems

Abstract

In this paper we address the problem of verifying in stochastic hybrid systems temporal logic properties whose probability of being true is very small -rare events. It is well known that sampling-based (Monte Carlo) techniques, such as statistical model checking, do not perform well for estimating rare-event probabilities. The problem is that the sample size required for good accuracy grows too large as the event probability tends to zero. However, several techniques have been developed to address this problem. We focus on importance sampling techniques, which bias the original system to compute highly accurate and efficient estimates. The main difficulty in importance sampling is to devise a good biasing density, that is, a density yielding a low-variance estimator. In this paper, we show how to use the cross-entropy method for generating approximately optimal biasing densities for statistical model checking. We apply the method with importance sampling and statistical model checking for estimating rare-event probabilities in stochastic hybrid systems coded as Stateflow/Simulink diagrams.

Statistical symbolic execution with informed sampling

“…Statistical hypothesis testing, being a randomized procedure operating on a limited number of samples, may produce false negatives or positives, i.e., it may reject a hypothesis that is actually true and vice versa. This problem can occur especially when the analyzed programs are very large and the probability of success or failure is close to the extremes (0 or 1) [36]. In the next section we show an instance of the problem.…”

“…In [15], SMC has been formulated as an estimation problem, with the number of samples fixed a priori by means of the Chernoff and Hoeffding bound [16]. Other approaches for deciding the number of samples have been discussed in [28,36]. Some of these approaches have been implemented in well-known probabilistic model checkers [18,32].…”

Compositional solution space quantification for probabilistic software analysis

“…Despite their generality, hit-or-miss Monte Carlo methods may suffer from a slow convergence rate [17], especially if the probability of the target event gets close to zero [32]. If additional information is known about the problem under analysis, it can be exploited to improve the estimation performance, i.e.…”

Importance Sampling for Stochastic Timed Automata

“…Researchers have thus turned to importance sampling. In [19] the authors consider rare event verification of a model of stochastic hybrid automata that shares a number of features in common with our own model. They suggest using the cross-entropy method [16] to refine a parametrised change of measure for importance sampling, but do not provide a means by which this can be applied to arbitrary hybrid systems.…”