Process calculus

In computer science, the process calculi (or process algebras) are a diverse family of related approaches for formally modelling concurrent systems. Process calculi provide a tool for the high-level description of interactions, communications, and synchronizations between a collection of independent agents or processes. They also provide algebraic laws that allow process descriptions to be manipulated and analyzed, and permit formal reasoning about equivalences between processes (e.g., using bisimulation). Leading examples of process calculi include CSP, CCS, ACP, and LOTOS. More recent additions to the family include the π-calculus, the ambient calculus, PEPA, the fusion calculus and the join-calculus. While the variety of existing process calculi is very large (including variants that incorporate stochastic behaviour, timing information, and specializations for studying molecular interactions), there are several features that all process calculi have in common: Representing interactions between independent processes as communication (message-passing), rather than as modification of shared variables. Describing processes and systems using a small collection of primitives, and operators for combining those primitives. Defining algebraic laws for the process operators, which allow process expressions to be manipulated using equational reasoning. To define a process calculus, one starts with a set of names (or channels) whose purpose is to provide means of communication. In many implementations, channels have rich internal structure to improve efficiency, but this is abstracted away in most theoretic models. In addition to names, one needs a means to form new processes from old ones. The basic operators, always present in some form or other, allow: parallel composition of processes specification of which channels to use for sending and receiving data sequentialization of interactions hiding of interaction points recursion or process replication Parallel composition of two processes and , usually written , is the key primitive distinguishing the process calculi from sequential models of computation.