CSL model checking algorithms for QBDs

Authors:
Anne Remke;Boudewijn R. Haverkort;Lucia Cloth
Affiliations:
University of Twente, Faculty for Electrical Engineering, Mathematics and Computer Science, PO Box 217, 7500 AE Enschede, The Netherlands;University of Twente, Faculty for Electrical Engineering, Mathematics and Computer Science, PO Box 217, 7500 AE Enschede, The Netherlands;University of Twente, Faculty for Electrical Engineering, Mathematics and Computer Science, PO Box 217, 7500 AE Enschede, The Netherlands
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

We present an in-depth treatment of model checking algorithms for a class of infinite-state continuous-time Markov chains known as quasi-birth death processes. The model class is described in detail, as well as the logic CSL to express properties of interest. Using a new property-independency concept, we provide model checking algorithms for all the CSL operators. Special emphasis is given to the time-bounded until operator for which we present a new and efficient computational procedure named uniformization with representatives. By the use of an application-driven dynamic stopping criterion, the algorithm stops whenever the property to be checked can be certified (or falsified). A comprehensive case study of a connection management system shows the versatility of our new algorithms.