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calculus of communicating systems : ウィキペディア英語版
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.
==Syntax==

Given a set of action names, the set of CCS processes is defined by the following BNF grammar:
:P ::= \emptyset\,\,\, | \,\,\,a.P_1\,\,\, | \,\,\,A\,\,\, | \,\,\,P_1+P_2\,\,\, | \,\,\,P_1|P_2\,\,\, | \,\,\,P_1()\,\,\, | \,\,\,P_1a\,\,\,
The parts of the syntax are, in the order given above
; empty process : the empty process \emptyset is a valid CCS process
; action : the process a.P_1 can perform an action a and continue as the process P_1
; process identifier : write A \overset} P_1 to use the identifier A to refer to the process P_1 (which may contain the identifier A itself, i.e., recursive definitions are allowed)
; choice : the process P_1+P_2 can proceed either as the process P_1 or the process P_2
; parallel composition : P_1|P_2 tells that processes P_1 and P_2 exist simultaneously
; renaming : P_1() is the process P_1 with all actions named a renamed as b
; restriction : P_1a is the process P_1 without action a

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