Calculus of Communicating Systems

  • V. S. Alagar
  • K. Periyasamy
Part of the Texts in Computer Science book series (TCS)


In automata theory, a process is modeled as an automaton. In Chaps.  6 and  7, we studied automata models for simple input/output systems with some extensions. In particular we discussed interaction of systems modeled by automata in Chap.  7. We modeled compositions of simple input/output systems as well as composition of reactive systems. In the latter instance, the composition is based on communication between automata, abstracted as “shared transitions”. The meaning of composed systems is understood from the behavior that can be observed. It is known to algebraists (Milner in A calculus for communicating systems, Lecture notes in computer science, vol 92. Springer, Berlin, 1980) that “the principle of compositionality of meaning requires an algebraic framework.” An algebra that allows equational reasoning about automata is the algebra of regular expressions. This is true for extended finite state machine models in which the semantics of concurrency includes all transitions, including synchronous communications whenever they occur.


Transition Rule Parallel Composition Label Transition System Derivation Tree Communicate Sequential Process 
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  1. 1.
    Baeten JCM (2003) Over 30 years of process algebra: past, present, and future. In: Accto L, Ésik Z, Fokkink W, Ingólfsdóttir A (eds) Process algebra: open problems and future directions. BRICS notes series, vol NS-03-3, pp 7–12 Google Scholar
  2. 2.
    Bergstra JA, Klop JW (1982) Fixed point semantics in process algebra. Technical report IW 208, Mathematical Center, Amsterdam Google Scholar
  3. 3.
    Bergstra JA, Klop JW (1984) Process algebra for synchronous communication. Inf Control 60(1):109–137 MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Bergstra JA, Klop JW (1985) Algebra of communicating processes with abstraction. Theor Comput Sci 37:77–121 MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Hewitt C, Baker H Jr. (1977) Actors and continuous functionals. MIT/LCS/TR-194 Google Scholar
  6. 6.
    Hoare CAR (1978) Communicating sequential processes. Commun ACM 21(8):666–677 MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Hoare CAR (1985) Communicating sequential processes. Prentice-Hall, New York MATHGoogle Scholar
  8. 8.
    Milner R (1980) A calculus for communicating systems. Lecture notes in computer science, vol 92. Springer, Berlin CrossRefGoogle Scholar
  9. 9.
    Milner R (1989) Communication and concurrency. Prentice-Hall, New York MATHGoogle Scholar
  10. 10.
    Milner R (1999) Communicating and mobile systems, the Pi-Calculus. Springer, Berlin MATHGoogle Scholar
  11. 11.
    Petri CA (1962) Kommunikation mit automaten. PhD Thesis, Institut fuer Instrumentelle Mathematik, Bonn Google Scholar
  12. 12.
    Petri CA (1980) Introduction to general net theory. In: Brauer W (ed) Proc advanced course on general net theory, processes, systems. Lecture notes in computer science, vol 84. Springer, Berlin, pp 1–20 Google Scholar
  13. 13.
    Walker D (1987) Introduction to a Calculus of communicating systems. Technical report ECS-LFCS-87-22, Department of Computer Science, University of Edinburgh, Edinburgh Google Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Dept. Computer Science and Software Eng.Concordia UniversityMontrealCanada
  2. 2.Computer Science DepartmentUniversity of Wisconsin-La CrosseLa CrosseUSA

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