Bisimulations and abstraction homomorphisms

  • Ilaria Castellani
Colloquium On Trees In Algebra And Programming Concurrency
Part of the Lecture Notes in Computer Science book series (LNCS, volume 185)


In this paper we show that the notion of bisimulation for a class of labelled transition systems (the class of nondeterministic processes) may be restated as one of “reducibility to a same system” via a simple reduction relation. The reduction relation is proven to enjoy some desirable properties, notably a Church-Rosser property. We also show that, when restricted to finite nondeterministic processes, the relation yields unique minimal forms for processes and can be characterised algebraically by a set of reduction rules.


Label Transition System Reduction Rule Concurrent Program Nondeterministic Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [BR]
    S. Brookes, C. Rounds (1983), “Behavioural Equivalence Relations induced by Program Logics”, in Proc. ICALP '83, LNCS 154.Google Scholar
  2. [C]
    Full version of this paper. Contact the author.Google Scholar
  3. [CFM]
    I. Castellani, P. Franceschi, U. Montanari (1982), “Labelled Event Structures: A Model for Observable Concurrency”, in: D. Bjorner (ed.):Proc. IFIP TC2 Working Conference on Formal Description of Programming Concepts II, Garmisch, June 1982: North-Holland Publ. Company 1983Google Scholar
  4. [DeN]
    R. De Nicola (1984), “Behavioural Equivalences for Transition Systems”, Internal Report I.E.I., Pisa, Italy.Google Scholar
  5. [HM]
    M. Hennessy, R. Milner (1983), “Algebraic laws for Nondeterminism and Concurrency”, Technical Report: CSR-133-83, University of Edinburgh.Google Scholar
  6. [K]
    R. Keller (1976), “Formal verification of Parallel Programs”, Communications of the ACM n. 19, Vol. 7.Google Scholar
  7. [M1]
    R. Milner (1980), A Calculus of Communicating Systems, LNCS 92.Google Scholar
  8. [M2]
    R. Milner (1982), “Calculi for Synchrony and Asynchrony”, J. Theoretical Computer Science, Vol. 25.Google Scholar
  9. [Pa]
    D. Park (1981), “Concurrency and Automata on Infinite Sequences”, in LNCS 104.Google Scholar
  10. [P]
    G. Plotkin (1981), “A Structured Approach to Operational Semantics”, DAIMI FN-19, Computer Science Dept, Aarhus University.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Ilaria Castellani
    • 1
  1. 1.Computer Science DepartmentUniversity of EdinburghUK

Personalised recommendations