Model checking of continuoustime Markov Chains against timed automata specifications
Chen, T. and Han, Tingting and Katoen, J.P. and Mereacre, A. and Jagadeesan, R. (2011) Model checking of continuoustime Markov Chains against timed automata specifications. Logical Methods in Computer Science 7 (1), ISSN 18605974.

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Abstract
We study the verification of a finite continuoustime Markov chain (CTMC) C against a linear realtime 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 singleclock 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 singleclock DTA specifications.
Metadata
Item Type:  Article 

School:  Birkbeck Schools and Departments > School of Business, Economics & Informatics > Computer Science and Information Systems 
Depositing User:  Administrator 
Date Deposited:  27 Feb 2014 11:15 
Last Modified:  27 Feb 2014 11:15 
URI:  http://eprints.bbk.ac.uk/id/eprint/9260 
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