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CONCUR’99 Concurrency Theory

Volume 1664 of the series Lecture Notes in Computer Science pp 146-161

Date:

Approximative Symbolic Model Checking of Continuous-Time Markov Chains

Extended Abstract
  • Christel BaierAffiliated withLehrstuhl für Praktische Informatik II, University of Mannheim
  • , Joost-Pieter KatoenAffiliated withLehrstuhl für Informatik 7, University of Erlangen-NürnbergSystems Validation Centre, University of Twente
  • , Holger HermannsAffiliated withSystems Validation Centre, University of Twente

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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 steadystate 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 timebounded 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.