Hierarchical counterexamples for discrete-time Markov chains

Authors:
Nils Jansen;Erika Ábrahám;Jens Katelaan;Ralf Wimmer;Joost-Pieter Katoen;Bernd Becker
Affiliations:
RWTH Aachen University, Germany;RWTH Aachen University, Germany;RWTH Aachen University, Germany;Albert-Ludwigs-University Freiburg, Germany;RWTH Aachen University, Germany;Albert-Ludwigs-University Freiburg, Germany
Venue:
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Year:
2011

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Abstract

This paper introduces a novel counterexample generation approach for the verification of discrete-time Markov chains (DTMCs) with two main advantages: (1) We generate abstract counterexamples which can be refined in a hierarchical manner. (2) We aim at minimizing the number of states involved in the counterexamples, and compute a critical subsystem of the DTMC whose paths form a counterexample. Experiments show that with our approach we can reduce the size of counterexamples and the number of computation steps by several orders of magnitude.