Connecting Algebraic and Logical Descriptions of Concurrent Systems

Algebraical approach and logical approach are two different methodologies for designing concurrent systems. In this paper, we show some connections between these two approaches. On one hand, we relate a set of primitives of process algebras which exactly corresponds to the primitives of basic process algebra (BPA for short) to the connectives of modal and temporal logics like fixpoint logic with chop (FLC for short). Thus, we can conclude that these logics could be used to compositionally develop complex systems in an algebra-like way. On the other hand, given a context-free process and an equivalence or preorder such as strong bisimulation, we present a uniform method to construct the characteristic formula of the process up to the relation directly from its syntax. So, all reductions concerning processes that are usually performed in an algebraical framework can be done in a logical framework.