Calculus of communicating systems

The calculus of communicating systems (CCS) is a process calculus introduced by Robin Milner around 1980 and the title of a book describing the calculus. Its actions model indivisible communications between exactly two participants. The formal language includes primitives for describing parallel composition, choice between actions and scope restriction. CCS is useful for evaluating the qualitative correctness of properties of a system such as deadlock or livelock. According to Milner, "There is nothing canonical about the choice of the basic combinators, even though they were chosen with great attention to economy. What characterises our calculus is not the exact choice of combinators, but rather the choice of interpretation and of mathematical framework". The expressions of the language are interpreted as a labelled transition system. Between these models, bisimilarity is used as a semantic equivalence. TOC Given a set of action names, the set of CCS processes is defined by the following BNF grammar: The parts of the syntax are, in the order given above inactive process the inactive process is a valid CCS process action the process can perform an action and continue as the process process identifier write to use the identifier to refer to the process (which may contain the identifier itself, i.e., recursive definitions are allowed) summation the process can proceed either as the process or the process parallel composition tells that processes and exist simultaneously renaming is the process with all actions named renamed as restriction is the process without action Communicating sequential processes (CSP), developed by Tony Hoare, is a formal language that arose at a similar time to CCS. The Algebra of Communicating Processes (ACP) was developed by Jan Bergstra and Jan Willem Klop in 1982, and uses an axiomatic approach (in the style of Universal algebra) to reason about a similar class of processes as CCS.