Weak stochastic bisimulation for non-Markovian processes

Abstract

In this paper we introduce a novel notion of bisimulation to properly capture the behavior of stochastic systems with general distributions. The key idea consists in the identification of different sequences of random variables if the additions of the random variables of each sequence are identically distributed. That is, we will not only identify sequences of internal actions with one of them (as it is usually done in weak bisimulations) but we will also reduce (in some conditions) sequences of stochastic transitions to only one transition. Therefore, we will identify processes that are considered non-equivalent in previous notions of bisimulation for this kind of languages. © Springer-Verlag Berlin Heidelberg 2005.