Backward Bisimulation in Markov Chain Model Checking

Equivalence relations can be used to reduce the state space of a system model, thereby permitting more efficient analysis. We study backward stochastic bisimulation in the context of model checking continuous-time Markov chains against Continuous Stochastic Logic (CSL) properties. While there are simple CSL properties that are not preserved when reducing the state space of a continuous-time Markov chain using backward stochastic bisimulation, we show that the equivalence can nevertheless be used in the verification of a practically significant class of CSL properties. We consider an extension of these results to Markov reward models and Continuous Stochastic Reward Logic. Furthermore, we identify the logical properties for which the requirement on the equality of state labeling sets (normally imposed on state equivalences in a model-checking context) can be omitted from the definition of the equivalence, resulting in a better state-space reduction.