Process Algebra and Dynamic Logic

Abstract

An extension of process algebra is introduced which can be compared to (propositional) dynamic logic. The additional feature is a ‘guard’ construct, related to the notion of a test in dynamic logic. This extension of process algebra is semantically based on processes that transform data, and its operational semantics is defined relative to a structure describing these transformations via transitions between pairs of a process term and a data-state. The data-states are given by a structure that also defines in which data-states guards hold and how actions (non-deterministically) transform these states. The operational semantics is studied modulo strong bisimulation equivalence. For basic process algebra (without operators for parallelism) a small axiom system is presented which is complete with respect to a general class of data environments. In case a data environment satisfies some expressiveness constraints, (local) bisimilarity can be completely axiomatized by adding three axioms to this system. Then process algebra with parallelism and guards is introduced. A two-phase calculus is provided that makes it possible to prove identities between parallel processes. Also this calculus is complete. The use of this calculus is demonstrated by an extended example. The last section of the paper consists of a short discussion on the operational meaning of the Kleene star operator. 1987 CR Categories: F.3.1, F.3.2, F.3.3, I.1.3.