calculus of communicating systems

Given a set of action names, the set of CCS processes is defined by the following BNF grammar:

:$P\; ::=\; 0\backslash ,\backslash ,\backslash ,\; |\; \backslash ,\backslash ,\backslash ,a.P\_1\backslash ,\backslash ,\backslash ,\; |\; \backslash ,\backslash ,\backslash ,A\backslash ,\backslash ,\backslash ,\; |\; \backslash ,\backslash ,\backslash ,P\_1+P\_2\backslash ,\backslash ,\backslash ,\; |\; \backslash ,\backslash ,\backslash ,P\_1|P\_2\backslash ,\backslash ,\backslash ,\; |\; \backslash ,\backslash ,\backslash ,P\_1[b/a]\backslash ,\backslash ,\backslash ,\; |\; \backslash ,\backslash ,\backslash ,P\_1\{\backslash backslash\}a\backslash ,\backslash ,\backslash ,$

The parts of the syntax are, in the order given above

; inactive process : the inactive process $0$ 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 $A\; \backslash overset\{\backslash underset\{\backslash mathrm\{def\}\}\{\}\}\{=\}\; P\_1$ 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)

; summation : 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 : $P\_1[b/a]$ is the process $P\_1$ with all actions named $a$ renamed as $b$

; restriction : $P\_1\{\backslash backslash\}a$ is the process $P\_1$ without action $a$

• 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.
• The pi-calculus, developed by Robin Milner, Joachim Parrow, and David Walker in the late 80's extends CCS with mobility of communication links, by allowing processes to communicate the names of communication channels themselves.
• PEPA, developed by Jane Hillston introduces activity timing in terms of exponentially distributed rates and probabilistic choice, allowing performance metrics to be evaluated.
• Reversible Communicating Concurrent Systems (RCCS) introduced by Vincent Danos, Jean Krivine, and others, introduces (partial) reversibility in the execution of CCS processes.

Some other languages based on CCS:

• Calculus of broadcasting systems
• Language Of Temporal Ordering Specification (LOTOS)
• Process Calculus for Spatially-Explicit Ecological Models (PALPS) is an extension of CCS with probabilistic choice, locations and attributes for locations

A Philippou, M Toro, M Antonaki. Simulation and Verification in a Process Calculus for Spatially-Explicit Ecological Models.

Scientific Annals of Computer Science 23 (1). 2014

• Java Orchestration Language Interpreter Engine (Jolie){{Cite journal |last=Montesi |first=Fabrizio |last2=Guidi |first2=Claudio |last3=Lucchi |first3=Roberto |last4=Zavattaro |first4=Gianluigi|date=2007-06-27|title=JOLIE: a Java Orchestration Language Interpreter Engine|journal=Electronic Notes in Theoretical Computer Science |series=Combined Proceedings of the Second International Workshop on Coordination and Organization (CoOrg 2006) and the Second International Workshop on Methods and Tools for Coordinating Concurrent, Distributed and Mobile Systems (MTCoord 2006) |volume=181 |pages=19–33|doi=10.1016/j.entcs.2007.01.051 |issn=1571-0661|doi-access=free }}

Models that have been used in the study of CCS-like systems:

• History monoid
• Actor model

• Robin Milner: A Calculus of Communicating Systems, Springer Verlag, {{ISBN|0-387-10235-3}}. 1980.
• Robin Milner, Communication and Concurrency, Prentice Hall, International Series in Computer Science, {{ISBN|0-13-115007-3}}. 1989

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Category:1980 in computing

Category:Process calculi