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Bounded Model Checking for GSMP Models of Stochastic Real-time Systems

Summary: Bounded Model Checking for GSMP Models of
Stochastic Real-time Systems
Rajeev Alur and Mikhail Bernadsky
Department of Computer and Information Science
University of Pennsylvania
{alur, mbernads}@cis.upenn.edu
Abstract. Model checking is a popular algorithmic verification technique for
checking temporal requirements of mathematical models of systems. In this pa-
per, we consider the problem of verifying bounded reachability properties of sto-
chastic real-time systems modeled as generalized semi-Markov processes (GSMP).
While GSMPs is a rich model for stochastic systems widely used in performance
evaluation, existing model checking algorithms are applicable only to subclasses
such as discrete-time or continuous-time Markov chains. The main contribution
of the paper is an algorithm to compute the probability that a given GSMP sat-
isfies a property of the form "can the system reach a target before time T within
k discrete events, while staying within a set of safe states". For this, we show
that the probability density function for the remaining firing times of different
events in a GSMP after k discrete events can be effectively partitioned into fi-
nitely many regions and represented by exponentials and polynomials. We report
on illustrative examples and their analysis using our techniques.


Source: Alur, Rajeev - Department of Computer and Information Science, University of Pennsylvania


Collections: Computer Technologies and Information Sciences