A Complete Axiomatization of Branching Bisimilarity for a Simple Process Language with Probabilistic Choice

Abstract

This paper proposes a notion of branching bisimilarity for non-deterministic probabilistic processes. In order to characterize the corresponding notion of rooted branching probabilistic bisimilarity, an equational theory is proposed for a basic, recursion-free process language with non-deterministic as well as probabilistic choice. The proof of completeness of the axiomatization builds on the completeness of strong probabilistic bisimilarity on the one hand and on the notion of a concrete process, i.e. a process that does not display (partially) inert $\tau$-moves, on the other hand. The approach is first presented for the non-deterministic fragment of the calculus and next generalized to incorporate probabilistic choice, too.

Written in 2019. Dedicated to Catuscia Palamidessi, on the occasion of her 60th birthday. Extended abstract in The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy - Essays Dedicated to Catuscia Palamidessi on the Occasion of Her 60th Birthday, LNCS 11760, Springer, 2019, pp. 139-162, doi:10.1007/978-3-030-31175-9_9