Correctness Issues of Symbolic Bisimulation Computation for Markov Chains

Bisimulation reduction is a classical means to fight the infamous state space explosion problem, which limits the applicability of automated methods for verification like model checking. A signature-based method, originally developed by Blom and Orzan for labeled transition systems and adapted for Markov chains by Derisavi, has proved to be very efficient. It is possible to implement it symbolically using binary decision diagrams such that it is able to handle very large state spaces efficiently. We will show, however, that for Markov chains this algorithm suffers from numerical instabilities, which often result in too large quotient systems. We will present and experimentally evaluate two different approaches to avoid these problems: first the usage of rational arithmetic, and second an approach not only to represent the system structure but also the transition rates symbolically. In addition, this allows us to modify their actual values after the quotient computation.