Hennessy-Milner Logic with recursion as a specification language, and a refinement calculus based on it

  • Sören Holmström
Part of the Workshops in Computing book series (WORKSHOPS COMP.)


This paper is about specification and verification of processes, modeled as CCSagents.We show, by means of examples that Hennessy-Milner Logic (HML) with recursion is a suitable language for expressing implicit specifications. By extending this specification language with refinement operators, i.e. operators that describe the internal structure of a system, we obtain a calculus for stepwise refinement of agents from a specification in HML to a realization in CCS. The method is demonstrated by proving the alternating-bit protocol under weak assumptions about the unreliable media.


Specification Language Operational Semantic Observable Behaviour Great Solution Proof Rule 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BR83]
    S. Brookes and W. Rounds, Behavioural equivalences induced by programming logics, ICALP’83, LNCS 154, 1983.Google Scholar
  2. [GS84]
    S. Graf and J. Sifakis, A modal characterization of observational congruence on finite terms of CCS, ICALP’84, LNCS 172.Google Scholar
  3. [HM85]
    M. Hennessy and R. Milner, Algebraic laws for Nondeterminism and Concurrency, JACM 32 (1), (1985).Google Scholar
  4. [Koze82]
    D. Kozen, Results on the Propositional µ-calculus, ICALP’82, LNCS 140.Google Scholar
  5. [Lars86]
    K.G. Larsen, Context-Dependent Bisimulation between processes, Ph. D. thesis CST 37–86, University of Edinburgh, 1986.Google Scholar
  6. [LM86]
    K. G. Larsen and R. Milner, A Complete Protocol Verification using Relativized Bisimulation, R 86–12, Institute of Electronic Systems, Aalborg University Center.Google Scholar
  7. [Lars87]
    K.G. Larsen, Proof Systems for Hennessy-Milner Logic with Recursion, to appear in CAAP’88.Google Scholar
  8. [Miln80]
    R. Milner, A Calculus of Communicating Systems, LNCS 92.Google Scholar
  9. [Miln83]
    R. Milner, Calculi for Synchrony and Asynchrony, Theoretical Computer Science 25 (1983) 267–310.MathSciNetMATHCrossRefGoogle Scholar
  10. [Miln84]
    R. Milner, The calculus CCS and its evaluation rules, Seminar on Concurrency, CMU, LNCS 197.Google Scholar
  11. [Wins85]
    G. Winskel, A Complete Proof System for SCCS with Modal Assertions, Cambridge Computer Lab., Techn. Rep. 78, September 1985.Google Scholar

Copyright information

© Springer-Verlag London 1990

Authors and Affiliations

  • Sören Holmström
    • 1
  1. 1.Programming Methodology Group, Dept. of Computer ScienceChalmers University of TechnologyGöteborgSweden

Personalised recommendations