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Step failures semantics and a complete proof system

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Summary

The (linear) failures semantics is a well-known model for the theoretical version of Hoare's CSP. We generalize this semantics by taking steps (i.e. multisets of simultaneously occurring actions) instead of single actions as the basic execution unit. Hence opposed to the linear semantics — where parallelism is modelled as arbitrary interleaving in order to avoid technical complication — the step failures semantics models parallelism explicitly and is equally easy to manage. In particular a sound and complete proof system is given. Opposed to the linear model divergence is treated uniformly here. The relation to the linear semantics can be established using our newly introduced deparallelize operator.

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References

  1. Arnold, A.: Synchronized behaviours of processes and rational relations. Acta Inf. 17, 21–29 (1982)

    Google Scholar 

  2. Austry, D., Boudol, G.: Algèbre de processus et synchronisation. Theor. Comput. Sci. 30, 91–131 (1984)

    Google Scholar 

  3. Brookes, S.D.: A model for communicating sequential processes, Ph.D. Thesis, Carnegia-Mellon Univ., Report CMU-CS-83-149 (1983)

  4. Brookes, S.D., Hoare, C.A.R., Roscoe, A.W.: A theory of communicating sequential processes. J. Assoc. Comput. Mach. 31, 560–599 (1984)

    Google Scholar 

  5. Brookes, S.D., Roscoe, A.W.: An improved failures model for communicating processes. In: Brookes, S.D., Roscoe, A.W., Winskel, G. (eds.) Seminar on concurrency. Proceedings, Pittsburgh 1984. (Lect. Notes Comput. Sci. 197, 281–305) Berlin Heidelberg New York: Springer 1985

  6. Broy, M.: Process semantics of communicating concurrent programs. Univ. Passau, Report MIP- 8602 (1986)

  7. Broy, M., Streicher, T.: Views of distributed systems. In: Venturini Zilli, M. (ed.) Mathematical models for the semantics of parallelism. Proceedings, Rome 1986. (Lect. Notes Comput. Sci. 280, 114–143) Berlin Heidelberg New York: Springer 1987

  8. Degano, P., De Nicola, R., Montanari, U.: CCS is an (augmented) contact free C/E-system. In: Venturini Zilli, M. (ed.) Mathematical models for the semantics of parallelism. Proceedings, Rome 1986. (Lect. Notes Comput. Sci. 280, 144–165) Berlin Heidelberg New York: Springer 1987

  9. Degano, P., De Nicola, R., Montanari, U.: A distributed operational semantics for CCS based on condition/event systems. Acta Inf. 26, 59–91 (1988)

    Google Scholar 

  10. Degano, P., Gorrieri, R., Marchetti, S.: An exercise in concurrency: A CSP process as a condition/ event system. In: Rozenberg, G. (ed.): Advances in Petri nets 1988. (Lect. Notes Comput. Sci. 340, 85–105) Berlin Heidelberg New York: Springer 1988

  11. De Nicola, R., Hennessy, M.C.B.: Testing equivalences for processes. Theor. Comput. Sci. 34, 83–133 (1984)

    Google Scholar 

  12. Elrad, T., Francez, N.: Decomposition of distributed programs into communication-closed layers. Sci. Comput. Program 2, 155–173 (1982)

    Google Scholar 

  13. Francez, N., Hoare, C.A.R., Lehmann, D.J., de Roever, W.P.: Semantics of nondeterminism, concurrency, and communication. J. Comput. Syst. Sci. 19, 290–308 (1979)

    Google Scholar 

  14. Francez, N., Lehmann, D., Pnueli, A.: A linear-history semantics for languages for distributed programming. Theor. Comput. Sci. 32, 25–46 (1984)

    Google Scholar 

  15. Glabbeck, R. van, Vaandrager, F.: Petri net models for algebraic theories of concurrency. In: de Bakker, J.W., Nijman, A.J., Treleaven, P.C. (eds.) PARLE, Parallel architectures and languages Europe. Vol. II. Processings, Eindhoven 1987. (Lect. Notes Comput. Sci. 259, 224–242) Berlin Heidelberg New York: Springer 1987

  16. Goltz, U.: On representing CCS programs by finite Petri nets. In: Chytil, M.P., Janiga, L., Koubek, V. (eds.) Mathematical foundations of computer science 1988. Proceedings, Carlsbad 1988. (Lect. Notes Comput. Sci. 324, 339–350) Berlin Heidelberg New York: Springer 1988

  17. Guessarian, I.: Algebraic semantics. (Lect. Notes Comput. Sci. 99) Berlin Heidelberg New York: Springer 1981

  18. Hennessy, M.C.B.: Algebraic theory of processes, 1st Ed. Cambridge, Massachusetts: MIT Press 1988

    Google Scholar 

  19. Hoare, C.A.R.: Communicating sequential processes. Commun. ACM 21, 666–677 (1978)

    Google Scholar 

  20. Kiehn, A.: On the interrelation between synchronized and non-synchronized behaviour of Petri nets. J. Inf. Process. Cybern. 24, 3–18 (1988)

    Google Scholar 

  21. Loogen, R.: Ein semantisches Modell für nichtdeterministische, parallele Prozesse. RWTH Aachen, Diploma Thesis 1985 (unpublished)

  22. Loogen, R., Goltz, U.: Modelling nondeterministic concurrent processes with event structures. Preliminary version available from RWTH Aachen, Report 87-15. Fund. Inf. 1987 (to appear)

  23. Milne, G.J.: CIRCAL and the representation of communication, concurrency, and time. ACM Trans. Program. Lang. Syst, 7, 270–298 (1985)

    Google Scholar 

  24. Milner, R.: A calculus of communicating systems. (Lect. Notes Comput. Sci. 92) Berlin Heidelberg New York: Springer 1980

  25. Milner, R.: Calculi for synchrony and asynchrony. Theor. Comput. Sci. 25, 267–310 (1983)

    Google Scholar 

  26. Nivat, M.: Behaviors of processes and synchronized systems of processes. In: Broy, M., Schmidt, G. (eds.) Theoretical foundations of programming methodology, pp. 473–551. Dordrecht: Reidel 1982

    Google Scholar 

  27. Olderog, E.-R.: Operational Petri net semantics for CCSP. In: Rozenberg, G. (ed.) Advances in Petri nets 1987. (Lect. Notes Comput. Sci. 266, 196–223) Berlin Heidelberg New York: Springer 1987

  28. Olderog, E.-R., Hoare, C.A.R.: Specification-oriented semantics for communicating processes. Acta Inf. 23, 9–66 (1986)

    Google Scholar 

  29. Plotkin, G.D.: An operational semantics for CSP. In: Bjørner, D. (ed.) Formal description of programming concepts-II. Proceedings, Garmisch-Partenkirchen 1982, pp. 199–223. Amsterdam: North-Holland 1983

    Google Scholar 

  30. Reisig, W.: On the semantics of Petri nets. In: Neuhold, E.J., Chroust, G. (eds.) Formal models in programming. Proceedings, Vienna 1985, pp. 347–372. Amsterdam: North-Holland 1985

    Google Scholar 

  31. Rozenberg, G., Verraedt, R.: Subset languages of Petri nets, Parts I and II. Theor. Comput. Sci. 26, 301–326 (1983) and 27, 85–108 (1983)

    Google Scholar 

  32. Salwicki, A., Müldner, T.: On the algorithmic properties of concurrent programs. In: Engeler, E. (ed.) Logic of programs. Proceedings, Zürich 1979. (Lect. Notes Comput. Sci. 125, 169–197) Berlin Heidelberg New York: Springer 1981

  33. Shields, M.W., Lauer, P.E.: A formal semantics for concurrent systems. In: Maurer, H.A. (ed.) Automata, languages and programming. Proceedings. Graz 1979. (Lect. Notes Comput. Sci. 71, 571–584) Berlin Heidelberg New York: Springer 1979

  34. Simone, R. de: Higher-level synchronising devices in MEIJE-SCCS. Theor. Comput. Sci. 37, 245- 267 (1985)

    Google Scholar 

  35. Taubner, D.: Two net-oriented semantics for TCSP. Univ. Hamburg, Report FBI-HH-B-116/85 (1985)

  36. Taubner, D.: Finite representations of CCS and TCSP programs by automata and Petri nets. (Lect. Notes Comput. Sci. 369) Berlin Heidelberg New York: Springer 1989

  37. Taubner, D., Vogler, W.: The step failure semantics. In: Brandenburg, F.J., Vidal-Naquet, G., Wirsing, M. (eds.) STACS 87. Proceedings, Passau 1987. (Lect. Notes Comput. Sci. 247, 348–359) Berlin Heidelberg New York: Springer 1987

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Author notes

  1. Dirk Taubner

    Present address: Siemens AG, ZTE IS INF 2, Otto-Hahn-Ring 6, D-8000, München 83

Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Arcisstrasse 21, D-8000, München 2, Federal Republic of Germany

    Dirk Taubner & Walter Vogler

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  1. Dirk Taubner
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  2. Walter Vogler
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Additional information

The first author is supported by an Ernst von Siemens scholarship. A preliminary version of this paper appeared in [37]

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Taubner, D., Vogler, W. Step failures semantics and a complete proof system. Acta Informatica 27, 125–156 (1989). https://doi.org/10.1007/BF00265151

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