Symbolic Counterexample Generation for Discrete-Time Markov Chains

  • Nils Jansen
  • Erika Ábrahám
  • Barna Zajzon
  • Ralf Wimmer
  • Johann Schuster
  • Joost-Pieter Katoen
  • Bernd Becker
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7684)


In this paper we investigate the generation of counterexamples for discrete-time Markov chains (DTMCs) and PCTL properties. Whereas most available methods use explicit representations for at least some intermediate results, our aim is to develop fully symbolic algorithms. As in most related work, our counterexample computations are based on path search. We first adapt bounded model checking as a path search algorithm and extend it with a novel SAT-solving heuristics to prefer paths with higher probabilities. As a second approach, we use symbolic graph algorithms to find counterexamples. Experiments show that our approaches, in contrast to other existing techniques, are applicable to very large systems with millions of states.


Target State Conjunctive Normal Form Path Search Binary Decision Diagram Satisfying Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Nils Jansen
    • 1
  • Erika Ábrahám
    • 1
  • Barna Zajzon
    • 1
  • Ralf Wimmer
    • 2
  • Johann Schuster
    • 3
  • Joost-Pieter Katoen
    • 1
  • Bernd Becker
    • 2
  1. 1.RWTH Aachen UniversityGermany
  2. 2.Albert-Ludwigs-University FreiburgGermany
  3. 3.University of the Federal Armed Forces MunichGermany

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