Approximate Symbolic Model Checking of Continuous-Time Markov Chains

  • Authors:
  • Christel Baier;Joost-Pieter Katoen;Holger Hermanns

  • Affiliations:
  • -;-;-

  • Venue:
  • CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
  • Year:
  • 1999

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Abstract

This paper presents a symbolic model checking algorithm for continuous-time Markov chains for an extension of the continuous stochastic logic CSL of Aziz et al [1]. The considered logic contains a time-bounded until-operator and a novel operator to express steady-state probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded until and the steady state-operator) and a Volterra integral equation system for time-bounded until. We propose a symbolic approximate method for solving the integrals using MTDDs (multi-terminal decision diagrams), a generalisation of MTBDDs. These new structures are suitable for numerical integration using quadrature formulas based on equally-spaced abscissas, like trapezoidal, Simpson and Romberg integration schemes.