Limits of Agents in Process Calculus
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Various behaviour equivalences are central notions in process calculus and in applications of process calculus, specification and implementation are expressed as two agents and correctness of programs is treated as a certain behaviour equivalence between specification and implementation. But many implementations can only approximate their formal definition of semantics and behaviour equivalences are not suitable concepts to characterize the mechanism of approximation of programs. As an attempt devoted to provide some useful tools for the understanding and analysis of approximate correctness of programs in concurrent systems, in this paper, we present a theory of limits of agents in process calculus. First, the concepts of strong and weak bisimulation limits and trace limits of agents are introduced and they may be used to describe evolution of softwares. Secondly, continuity of various combinators in process calculus with respect to these notions of limits are shown. A complex concurrent system always consists of several subsystems. Whenever this system needs to be revised step by step to reach a certain requirement, we hope to do this in a structural (or modular) way, i.e., we would like to revise it component by component. The result in regard to continuity of combinators puts this intuitive idea on a firm basis. Thirdly, we demonstrate that strong and weak bisimulation limits preserve determinacy and confluency of agents.
KeywordsProcess calculus bisimulation trace semantic equivalence net limit continuity determinacy confluency solution of equation
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