On Kleene Algebra vs. Process Algebra

04/10/2023

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by   Yong Wang, et al.

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We try to clarify the relationship between Kleene algebra and process algebra, based on the very recent work on Kleene algebra and process algebra. Both for concurrent Kleene algebra (CKA) with communications and truly concurrent process algebra APTC with Kleene star and parallel star, the extended Milner's expansion law a∥ b=a· b+b· a+a∥ b +a| b holds, with a,b being primitives (atomic actions), ∥ being the parallel composition, + being the alternative composition, · being the sequential composition and the communication merge | with the background of computation. CKA and APTC are all the truly concurrent computation models, can have the same syntax (primitives and operators), maybe have the same or different semantics.