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ACPτ a universal axiom system for process specification

  • Part IV An Algebraic Approach To Concurrency
  • Conference paper
  • First Online:
Algebraic Methods: Theory, Tools and Applications (Algebraic Methods 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 394))

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Abstract

Starting with Basic Process Algebra (BPA), an axiom system for alternative composition (+) and sequential composition (·) of processes, we give a presentation in several intermediate stages leading to ACPτ, Algebra of Communicating Processes with abstraction. At each successive stage an example is given showing that the specification power is increased. Also some graph models for the respective axiom systems are informally presented. We conclude with the Finite Specification Theorem for ACPτ, stating that each finitely branching, effectively presented process (as an element of the graph model) can be specified in ACPτ by means of a finite system of guarded recursion equations.

Note: This paper is reprinted with kind permission of the CWI Newsletter and the Centre for Mathematics and Computer Science from Issue no. 15 of the CWI Newsletter (June 1987).

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References

  1. J.C.M. Baeten, J.A. Bergstra, J.W. Klop (1987). On the consistency of Koomen's Fair Abstraction Rule. TCS 51 (1/2), 129–176.

    Article  Google Scholar 

  2. J.C.M. Baeten, J.A. Bergstra, J.W. Klop (1987). Decidability of bisimulation equivalence for processes generating context-free languages. J.W. de Bakker, A.J. Nijman, P.C. Treleaven (eds.). Proceedings of the PARLE Conference, Eindhoven 1987, Vol. II, Springer LNCS 259, 94–113.

    Google Scholar 

  3. J.C.M. Baeten, R.J. van Glabbeek (1987). Abstraction and Empty Process in Process Algebra, CWI Report CS-R8721, Centre for Mathematics and Computer Science, Amsterdam.

    Google Scholar 

  4. J.A. Bergstra, J.W. Klop (1984). The algebra of recursively defined processes and the algebra of regular processes. J. Paredaens (ed.). Proc. 11th ICALP, Antwerpen 1984, Springer LNCS 172, 82–95.

    Google Scholar 

  5. J.A. Bergstra, J.W. Klop (1986). Algebra of communicating processes. J.W. de Bakker, M. Hazewinkel, J.K. Lenstra (eds.). CWI Monograph I, Proceedings of the CWI Symposium Mathematics and Computer Science, North-Holland, Amsterdam, 89–138.

    Google Scholar 

  6. J.A. Bergstra, J.W. Klop (1986). Process algebra: specification and verification in bisimulation semantics. M. Hazewinkel, J.K. Lenstra, L.G.L.T. Meertens (eds.). CWI Monograph 4, Proceedings of the CWI Symposium Mathematics and Computer Science II, North-Holland, Amsterdam, 61–94.

    Google Scholar 

  7. J.A. Bergstra, J.W. Klop, E.-R. Olderog (1987). Failures without chaos: a new process semantics for fair abstraction. M. Wirsing (ed.). Proceedings IFIP Conference on Formal Description of Programming Concepts, Gl. Avernaes 1986, North-Holland, Amsterdam, 77–103.

    Google Scholar 

  8. R.J. van Glabbeek, F.W. Vaandrager (1987). Petri net models for algebraic theories of concurrency. J.W. de Bakker, A.J. Nijman, P.C. Treleaven (eds.). Proc. PARLE Conference, Eindhoven 1987, Vol. II, Springer LNCS 259, 224–242.

    Google Scholar 

  9. C.P.J. Koymans, J.C. Mulder (1986). A Modular Approach to Protocol Verification using Process Algebra, Logic Group Preprint Series Nr.6, Dept. of Philosophy, State University of Utrecht.

    Google Scholar 

  10. L. Kossen, W.P. Weijland (1987). Correctness Proofs for Systolic Algorithms: Palindromes and Sorting, Report FVI 87-04, Computer Science Department, University of Amsterdam.

    Google Scholar 

  11. S. Mauw (1987). A Constructive Version of the Approximation Induction Principle, Report FVI 87-09, Computer Science Department, University of Amsterdam.

    Google Scholar 

  12. R. Milner (1980). A Calculus of Communicating Systems, Springer LNCS 92.

    Google Scholar 

  13. D. Park (1981). Concurrency and automata on infinite sequences. Proc. 5th GI Conference, Springer LNCS 104.

    Google Scholar 

  14. F.W. Vaandrager (1986). Verification of Two Communication Protocols by Means of Process Algebra, CWI Report CS-R8608, Centre for Mathematics and Computer Science, Amsterdam.

    Google Scholar 

  15. W.P. Weijland (1987). A Systolic Algorithm for Matrix-Vector Multiplication, Report FVI 87-08, Computer Science Department, University of Amsterdam.

    Google Scholar 

  16. J.L.M. Vrancken (1986). The Algebra of Communicating Processes with Empty Process, Report FVI 86-01, Computer Science Department, University of Amsterdam.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Amsterdam, P.O. Box 19268, 1000 GG, Amsterdam

    J. A. Bergstra

  2. Department of Philosophy, State University of Utrecht, P.O. Box 8810, 3508 TA, Utrecht

    J. A. Bergstra

  3. Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB, Amsterdam

    J. W. Klop

  4. Department of Mathematics and Computer Science, Free University, De Boelelaan 1081, 1081 HV, Amsterdam

    J. W. Klop

Authors
  1. J. A. Bergstra
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  2. J. W. Klop
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Martin Wirsing Jan A. Bergstra

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© 1989 Springer-Verlag Berlin Heidelberg

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Bergstra, J.A., Klop, J.W. (1989). ACPτ a universal axiom system for process specification. In: Wirsing, M., Bergstra, J.A. (eds) Algebraic Methods: Theory, Tools and Applications. Algebraic Methods 1987. Lecture Notes in Computer Science, vol 394. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015048

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  • DOI: https://doi.org/10.1007/BFb0015048

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51698-9

  • Online ISBN: 978-3-540-46758-8

  • eBook Packages: Springer Book Archive

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