Chen, Taolue and Han, Tingting and Katoen, Joost-Pieter and Mereacre, Alexandru - Model Checking of Continuous-Time Markov Chains Against Timed Automata Specifications

lmcs:697 - Logical Methods in Computer Science, March 29, 2011, Volume 7, Issue 1
Model Checking of Continuous-Time Markov Chains Against Timed Automata Specifications

Authors: Chen, Taolue and Han, Tingting and Katoen, Joost-Pieter and Mereacre, Alexandru

We study the verification of a finite continuous-time Markov chain (CTMC) C against a linear real-time specification given as a deterministic timed automaton (DTA) A with finite or Muller acceptance conditions. The central question that we address is: what is the probability of the set of paths of C that are accepted by A, i.e., the likelihood that C satisfies A? It is shown that under finite acceptance criteria this equals the reachability probability in a finite piecewise deterministic Markov process (PDP), whereas for Muller acceptance criteria it coincides with the reachability probability of terminal strongly connected components in such a PDP. Qualitative verification is shown to amount to a graph analysis of the PDP. Reachability probabilities in our PDPs are then characterized as the least solution of a system of Volterra integral equations of the second type and are shown to be approximated by the solution of a system of partial differential equations. For single-clock DTA, this integral equation system can be transformed into a system of linear equations where the coefficients are solutions of ordinary differential equations. As the coefficients are in fact transient probabilities in CTMCs, this result implies that standard algorithms for CTMC analysis suffice to verify single-clock DTA specifications.


Source : oai:arXiv.org:1101.3694
DOI : 10.2168/LMCS-7(1:12)2011
Volume: Volume 7, Issue 1
Published on: March 29, 2011
Submitted on: December 25, 2009
Keywords: Computer Science - Logic in Computer Science,D.2.4


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