Logical characterization of branching bisimilarity over random processes

Abstract

Quantitative aspects like probabilities play an important role in concurrent processes. Providing a (modal) logic for a randomized concurrency model can augment the toolbox of analyzing probabilistic processes, and thus is a frequent topic in the field. In this paper, we are interested in logically characterizing uniformly randomized processes, whose semantical behavior is defined in a model-independent manner. Specifically, we present two modal logics for the uniformly randomized version of finite-state CCS (RCCS_fsfor short). Our logics extend the Hennessy-Milner logic, and one of them is equipped with the μ operator. Indeed, we prove that both logics characterize the branching bisimilarity for RCCS_fs, i.e., two RCCS_fsprocesses are branching bisimilar if and only if they are logically equivalent. To facilitate the proof, we also develop for RCCS_fsan up-to proof method, which may be of independent interest.