Calculus of communicating systems

The calculus of communicating systems 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.


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
; empty process : the empty 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
; choice : 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

Related calculi, models, and languages

Some other languages based on CCS:
Models that have been used in the study of CCS-like systems: