Skip to main content
SpringerLink
Log in

A refinement calculus for specifications in Hennessy-Milner logic with recursion

  • Published:
Formal Aspects of Computing

Abstract

This paper is about specification and verification of processes, modelled as CCS-agents. We show, by means of examples that Hennessy-Milner Logic (HML) with recursion is a suitable language for expressing implicit or partial specifications. By extending this specification language withrefinement 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 realisation in CCS. The method is demonstrated by proving the alternating-bit protocol under weak assumptions about the unreliable media.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Brookes, S. and Rounds, W.: Behavioural equivalences induced by programming logics,ICALP'83, LNCS 154, Springer-Verlag, 1983.

  2. Graf, S. and Sifakis, J.: A modal characterization of observational congruence on finite terms of CCS,ICALP'84, LNCS 172, Springer-Verlag, 1984.

  3. Hennessy, M. and Milner, R.: Algebraic laws for Nondeterminism and Concurrency.J. ACM, 32(1) (1985).

  4. Kozen, D.: Results on the Propositionalμ-calculus,ICALP'82, LNCS 140, Springer-Verlag, 1982.

  5. Larsen, K.G.: Context-Dependent Bisimulation between Processes, Ph.D. thesis CST-37-86, University of Edinburgh, 1986.

  6. Larsen, K.G.: Proof Systems for Hennessy-Milner Logic with Recursion,CAAP'88, LNCS 299, Springer-Verlag, 1988.

  7. Larsen, K. G. and Milner, R.: A Complete Protocol Verification using Relativized Bisimulation, R86-12, Institute of Electronic Systems, Aalborg University Center, 1986.

  8. Milner, R.:A Calculus of Communicating Systems, LNCS 92, Springer-Verlag, 1980.

  9. Milner, R.: Calculi for Synchrony and Asynchrony.Theoretical Computer Science, 25, 267–310 (1983).

    Google Scholar 

  10. Milner, R.: The calculus CCS and its evaluation rules,Seminar on Concurrency, CMU, LNCS 197, Springer-Verlag, 1984.

  11. Pnueli, A.: Linear and Branching Structures in the Semantics and Logics of Reactive Systems,ICALP'85, LNCS 194, Springer-Verlag, 1985.

  12. Stirling, C.: A Proof Theoretic Characterisation of Observational Equivalence,Theoretical Computer Science 39 (1985).

  13. Stirling, C.: A Complete Compositional Modal Proof System for a Subset of CCS,ICALP'85, LNCS 194, Springer-Verlag, 1985.

  14. Tarski, A.: A Lattice-Theoretical Fixpoint Theorem and its Applications,Pacific J. Math. 5 (1955).

  15. Winskel, G.: A Complete Proof System for SCCS with Modal Assertions, Cambridge Computer Lab., Tech. Rep. 78, September 1985.

Download references

Author information

Authors and Affiliations

  1. Programming Methodology Group, Department of Computer Science, Chalmers University of Technology, S-412 96, Göteborg, Sweden

    Sören Holmström

Authors
  1. Sören Holmström
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Holmström, S. A refinement calculus for specifications in Hennessy-Milner logic with recursion. Formal Aspects of Computing 1, 242–272 (1989). https://doi.org/10.1007/BF01887208

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01887208

Key words

Search

Navigation