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arXiv · 2502.05631

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

Rob van Glabbeek·Jan Friso Groote·Erik de Vink
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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.

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Rob van Glabbeek, Jan Friso Groote, Erik de Vink. 2025-02-08. A Complete Axiomatization of Branching Bisimilarity for a Simple Process Language with Probabilistic Choice. https://arxiv.org/abs/2502.05631

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