Finite horizon analysis of Markov Chains with the Murϕ verifier

  • Giuseppe Della Penna
  • Benedetto Intrigila
  • Igor Melatti
  • Enrico Tronci
  • Marisa Venturini Zilli
Special section on Recent Advances in Hardware Verification

Abstract

In this paper we present an explicit disk-based verification algorithm for Probabilistic Systems defining discrete time/finite state Markov Chains. Given a Markov Chain and an integer k (horizon), our algorithm checks whether the probability of reaching an error state in at most k steps is below a given threshold. We present an implementation of our algorithm within a suitable extension of the Murϕ verifier. We call the resulting probabilistic model checker FHP-Murϕ (Finite Horizon ProbabilisticMurϕ). We present experimental results comparing FHP-Murϕ with (a finite horizon subset of) PRISM, a state-of-the-art symbolic model checker for Markov Chains. Our experimental results show that FHP-Murϕ can handle systems that are out of reach for PRISM, namely those involving arithmetic operations on the state variables (e.g. hybrid systems).

Keywords

Automatic verification Model checking Markov chains Probabilistic model checking Probabilistic verification 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Giuseppe Della Penna
    • 1
  • Benedetto Intrigila
    • 3
  • Igor Melatti
    • 1
  • Enrico Tronci
    • 2
  • Marisa Venturini Zilli
    • 2
  1. 1.Dipartimento di InformaticaUniversità di L’AquilaCoppitoItaly
  2. 2.Dipartimento di InformaticaUniversità di Roma “La Sapienza”RomeItaly
  3. 3.Dipartimento di Matematica Pura ed ApplicataUniversità di Roma “Tor Vergata”RomeItaly

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