On Weak Bisimilarities in CCSK

2026-08-11

AI Summary

This work addresses the lack of systematic investigation into the directionality of τ-actions within weak reversible bisimulations in the reversible process calculus CCSK. To tackle this gap, the paper introduces two novel notions of weak reversible bisimulation—directional and mixed bisimulation—and rigorously analyzes their properties using bisimulation theory and algebraic techniques. Notably, the mixed bisimulation is shown to be a congruence and capable of fully abstracting away τ-actions, thereby establishing a robust theoretical foundation for behavioral equivalence in reversible computation. This contribution fills a critical theoretical void concerning weak reversible equivalences in CCSK and significantly advances the formal semantics of reversible concurrent systems.

Abstract

In the context of CCSK, a reversible extension of CCS, we study different notions of bisimilarity (strong/weak, forward-only/reversible) and highlight their differences and commonalities. In particular, for the weak reversible case, not previously studied in the literature, we propose two variants, dubbed directional and mixed bisimilarity, depending on whether $τ$ actions should be in the same direction (forward/backward) as the action being matched or not. We show, in particular, that mixed bisimilarity is a congruence and completely abstracts away from $τ$ actions.

Problem

• weak bisimilarity
• reversible CCS
• tau actions
• directional bisimilarity
• mixed bisimilarity

Innovation

• reversible CCS
• weak bisimilarity
• mixed bisimilarity
• directional bisimilarity
• congruence