On Weak Bisimilarities in CCSK

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 $\tau$ 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 $\tau$ actions.