Finite horizon analysis of Markov Chains with the Murϕ verifier

  • Authors:
  • Giuseppe Della Penna;Benedetto Intrigila;Igor Melatti;Enrico Tronci;Marisa Venturini Zilli

  • Affiliations:
  • Università di L’Aquila, Dipartimento di Informatica, 67100, Coppito, L’Aquila, Italy;Università di Roma “Tor Vergata”, Dipartimento di Matematica Pura ed Applicata, Via della Ricerca Scientifica 1, 00133, Rome, L’Aquila, Italy;Università di L’Aquila, Dipartimento di Informatica, 67100, Coppito, L’Aquila, Italy;Università di Roma “La Sapienza”, Dipartimento di Informatica, Via Salaria 113, 00198, Rome, L’Aquila, Italy;Università di Roma “La Sapienza”, Dipartimento di Informatica, Via Salaria 113, 00198, Rome, L’Aquila, Italy

  • Venue:
  • International Journal on Software Tools for Technology Transfer (STTT) - A View from Formal Methods 2003 (pp 301-354); Special Section on Recent Advances in Hardware Verification (pp 355-447)
  • Year:
  • 2006

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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).