Abstract
Generation of counterexamples is a highly important task in the model checking process. In contrast to, e.,g., digital circuits where counterexamples typically consist of a single path leading to a critical state of the system, in the probabilistic setting counterexamples may consist of a large number of paths. In order to be able to handle large systems and to use the capabilities of modern SAT-solvers, bounded model checking (BMC) for discrete-time Markov chains was established.
In this paper we introduce the usage of SMT-solving over linear real arithmetic for the BMC procedure. SMT-solving, extending SAT with theories in this context on the one hand leads to a convenient way to express conditions on the probability of certain paths and on the other hand allows to handle Markov reward models. We use the former to find paths with high probability first. This leads to more compact counterexamples. We report on some experiments, which show promising results.
This work was partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS) and the DFG-Project “CEBug – CounterExample Generation for Stochastic Systems using Bounded Model Checking”.
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Braitling, B., Wimmer, R., Becker, B., Jansen, N., Ábrahám, E. (2011). Counterexample Generation for Markov Chains Using SMT-Based Bounded Model Checking. In: Bruni, R., Dingel, J. (eds) Formal Techniques for Distributed Systems. FMOODS FORTE 2011 2011. Lecture Notes in Computer Science, vol 6722. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21461-5_5
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