Bisimulation minimisation mostly speeds up probabilistic model checking

Abstract

This paper studies the effect of bisimulation minimisation in model checking of monolithic discrete-time and continuous-time Markov chains as well as variants thereof with rewards. Our results show that-as for traditional model checking-enormous state space reductions (up to logarithmic savings) may be obtained. In contrast to traditional model checking, in many cases, the verification time of the original Markov chain exceeds the quotienting time plus the verification time of the quotient. We consider probabilistic bisimulation as well as versions thereof that are tailored to the property to be checked. © Springer-Verlag Berlin Heidelberg 2007.