Counterexamples in Probabilistic LTL Model Checking for Markov Chains

  • Matthias Schmalz
  • Daniele Varacca
  • Hagen Völzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5710)


We propose a way of presenting and computing a counterexample in probabilistic LTL model checking for discrete-time Markov chains. In qualitative probabilistic model checking, we present a counterexample as a pair (α,γ), where α,γ are finite words such that all paths that extend α and have infinitely many occurrences of γ violate the specification. In quantitative probabilistic model checking, we present a counterexample as a pair (W,R), where W is a set of such finite words α and R is a set of such finite words γ. Moreover, we suggest how the counterexample presented helps the user identify the underlying error in the system by means of an interactive game with the model checker.


Markov Chain Model Check Markov Decision Process Linear Temporal Logic Atomic Proposition 


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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Matthias Schmalz
    • 1
  • Daniele Varacca
    • 2
  • Hagen Völzer
    • 3
  1. 1.ETH ZurichSwitzerland
  2. 2.PPS - CNRS & Univ. Paris DiderotFrance
  3. 3.IBM Zurich Research LaboratorySwitzerland

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