On divergence-sensitive weak probabilistic bisimilarity

Abstract

Weak probabilistic bisimilarity is a well-established notion to equate concurrent probabilistic systems that behave observably equivalent. This notion can be pivotal in the model checking of large probabilistic systems, because the considered model can be replaced by an equivalent, but possibly much smaller one prior to model checking. The conventional work has thus far considered weak probabilistic bisimilarity while ignoring the divergent behavior (interpreted as infinite internal computations). However, we argue that divergence can have a remarkable influence on the equivalence of two concurrent probabilistic systems. We thus explore divergence-sensitive refinements of weak probabilistic bisimilarity. We work in the setting of probabilistic automata, and study the consistent feasible verification method for the notion of divergence-sensitivity that discriminates presence and absence of divergence in bisimilar states. We furthermore present a novel polynomial-time algorithm to compute divergence-sensitive bisimilarity. It intertwines partition-refinement and inductive verification steps in a highly non-trivial manner.