Shortest Counterexamples for Symbolic Model Checking of LTL with Past

  • Viktor Schuppan
  • Armin Biere
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3440)


Shorter counterexamples are typically easier to understand. The length of a counterexample, as reported by a model checker, depends on both the algorithm used for state space exploration and the way the property is encoded. We provide necessary and sufficient criteria for a Büchi automaton to accept shortest counterexamples. We prove that Büchi automata constructed using the approach of Clarke, Grumberg, and Hamaguchi accept shortest counterexamples of future time LTL formulae, while an automaton generated with the algorithm of Gerth et al. (GPVW) may lead to unnecessary long counterexamples. Optimality is lost in the first case as soon as past time operators are included. Adapting a recently proposed encoding for bounded model checking of LTL with past, we construct a Büchi automaton that accepts shortest counterexamples for full LTL. We use our method of translating liveness into safety to find shortest counterexamples with a BDD-based symbolic model checker without modifying the model checker itself. Though our method involves a quadratic blowup of the state space, it outperforms SAT-based bounded model checking on a number of examples.


Model Check Linear Temporal Logic Loop Iteration Atomic Proposition Kripke Structure 
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 2005

Authors and Affiliations

  • Viktor Schuppan
    • 1
  • Armin Biere
    • 2
  1. 1.Computer Systems InstituteETH ZürichZürichSwitzerland
  2. 2.Institute for Formal Models and VerificationJohannes Kepler UniversityLinzAustria

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