Bisimulation and Trace Limits of Agents

Abstract

In this chapter, we start our study of topology in process calculus. In an attempt to provide some useful mathematical tools for the understanding and analysis of infinite evolution of concurrent programs, we examine a theory of limits of agents in process calculus. The concepts of strong and weak bisimulation limits and trace limits of agents are introduced and these limits are shown to form a convergence class (see Kelley [1955], Chapter 2), so they induce so-called strong and weak bisimulation topologies and trace topology, respectively. These notions of limits can be used to describe the evolution of software as well as biological systems in which information is exchanged between cells. Furthermore, continuity of various combinators in process calculus with respect to these notions of limits is shown in respective sections.