Topology in Process Calculus : Approximate Correctness and Infinite Evolution of Concurrent Programs

Process calculi are among the most successful models of concurrent systems. Various behavior equivalences between processes are central notions in CCS (calculus of communicating systems) and other process calculi. In the real applications, specification and implementation are described as two processes, and correctness of programs is treated as a certain behavior equivalence between them. The purpose of this book is to establish a theory of approximate correctness and infinite evolution of concurrent programs by employing some notions and tools from point-set topology. This book is restricted to CCS for simplicity, but the main idea also applies to some other process calculi. The concept of bisimulation limits, useful for the understanding and analysis of infinite evolution of processes, is introduced. In addition, the notions of near bisimulations and bisimulation indexes, suitable in describing approximate correctness of concurrent programs, are proposed. The book will be of particular interest to researchers in the fields of theoretical computer science, especially theory of concurrency and hybrid systems, and graduate students in related disciplines. It will also be valuable to practical system designers developing concurrent and/or real-time systems.