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Bayesian statistical model checking with application to Stateflow/Simulink verification

Lookup NU author(s): Dr Paolo Zuliani


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We address the problem of model checking stochastic systems, i.e., checking whether a stochastic system satisfies a certain temporal property with a probability greater (or smaller) than a fixed threshold. In particular, we present a Statistical Model Checking (SMC) approach based on Bayesian statistics. We show that our approach is feasible for a certain class of hybrid systems with stochastic transitions, a generalization of Simulink/Stateflow models. Standard approaches to stochastic discrete systems require numerical solutions for large optimization problems and quickly become infeasible with larger state spaces. Generalizations of these techniques to hybrid systems with stochastic effects are even more challenging. The SMC approach was pioneered by Younes and Simmons in the discrete and non-Bayesian case. It solves the verification problem by combining randomized sampling of system traces (which is very efficient for Simulink/Stateflow) with hypothesis testing (i.e., testing against a probability threshold) or estimation (i.e., computing with high probability a value close to the true probability). We believe SMC is essential for scaling up to large Stateflow/Simulink models. While the answer to the verification problem is not guaranteed to be correct, we prove that Bayesian SMC can make the probability of giving a wrong answer arbitrarily small. The advantage is that answers can usually be obtained much faster than with standard, exhaustive model checking techniques. We apply our Bayesian SMC approach to a representative example of stochastic discrete-time hybrid system models in Stateflow/Simulink: a fuel control system featuring hybrid behavior and fault tolerance. We show that our technique enables faster verification than state-of-the-art statistical techniques. We emphasize that Bayesian SMC is by no means restricted to Stateflow/Simulink models. It is in principle applicable to a variety of stochastic models from other domains, e.g., systems biology.

Publication metadata

Author(s): Zuliani P, Platzer A, Clarke EM

Publication type: Article

Publication status: Published

Journal: Formal Methods in System Design

Year: 2013

Volume: 43

Issue: 2

Pages: 338-367

Print publication date: 01/10/2013

ISSN (print): 0925-9856

ISSN (electronic): 1572-8102

Publisher: Springer


DOI: 10.1007/s10703-013-0195-3


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Funder referenceFunder name
1041377GigaScale Research Center
2005TJ1366Semiconductor Research Corporation
CNS0931985National Science Foundation
CNS1054246National Science Foundation
CNS0926181National Science Foundation
GMCMUCRLNV301General Motors
N000141010188Office of Naval Research