Comparative analysis of bisimulation relations on alternating and non-alternating probabilistic models

Abstract

We consider bisimulation and weak bisimulation relations in the context of the labeled Markov chains of Hansson and Jonsson, the concurrent labeled Markov chains of Philippou, Lee, and Sokolsky, and the probabilistic automata of Segala. We identify a taxonomy of bisimulation relations that captures the existing definitions for each one of the three models, and we compare the relations within each model and across models. The comparison across models is given according to a notion of embedding, where we order the three models by generality and we view objects in less general models as objects of more general models.