Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T09:06:30.493Z Has data issue: false hasContentIssue false
  • English
  • Français

Step bisimulation is pomset equivalence on a parallel language without explicit internal choice

Published online by Cambridge University Press:  04 March 2009

Douglas R. Troeger
Douglas R. Troeger
Affiliation:
Department of Computer Sciences, The City College of New York, Convent Avenue at 138th Street, New York, NY 10031
Get access Rights & Permissions [Opens in a new window]

Abstract

We focus attention on a language ℒ generated by a set of elementary actions under operations of sequential composition, external binary choice, iteration, and non-nested disjoint parallel composition: that is, on an especially simple parallel language without explicit internal, or ‘local’, nondeterminism. ℒ is nondeterministic, despite the restriction to external choice, since a given action may occur in both subterms F and G of the parallel composition F ║ G. We exhibit a single set of equations that axiomatizes both step bisimulation and pomset equivalence on ℒ Given that step bisimulation and pomset equivalence are incomparable on the language ℒ+ obtained from ℒ by relaxing just the constraint on choice, the coincidence of these equivalences on ℒ suggests that the elimination of explicit internal choice can result in simplifications at the semantic level. We reinforce this impression by showing for ℒ that step bisimulation (i) coincides with pomset bisimulation equivalence, (ii) is real-time consistent, and (iii) has step trees as concrete representatives of its equivalence classes. Moreover, we show that none of these results holds for the language ℒ+ Finally, step trace equivalence is proved not to coincide with step bisimulation equivalence on ℒ.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 3 , Issue 1 , March 1993 , pp. 25 - 62
Copyright
Copyright © Cambridge University Press 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramsky, S. (1981) Eliminating Local Non-Determinism: A New Semantics for CCS, Report 290, Computer Systems Laboratory, Queen Mary College, London.Google Scholar
Aceto, L. (1991) Full Abstraction for Series-Parallel Pomsets. In: Proceedings TAPSOFT 91. Springer-Verlag LNCS 493.Google Scholar
Arnold, A. and Nivat, M. (1980) The Metric Space of Infinite Trees. Algebraic and Topological Properties. Annales Societatis Mathematicae Polonae, Series IV. Fund. Inf. III 445–476.Google Scholar
Bergstra, J. A. and Klop, J. W. (1984) Process Algebra for Synchronous Communication. Information and Control 60 109–137.CrossRefGoogle Scholar
Best, E. (1987) COSY: Its Relationship to Nets and to CSP. Springer-Verlag LNCS 255 416–440.Google Scholar
Best, E., Devillers, R., Kiehn, A. and Pomello, L. (1991) Concurrent Bisimulation in Petri Nets. Acta Inf. 28 231–264.CrossRefGoogle Scholar
Bloom, S. and Tindell, R. (1979) Algebraic and Graph Theoretic Characterizations of Structured Flowchart Schemes. Theoretical Comp. Sci. 9 265–286.CrossRefGoogle Scholar
Boudol, G. (1985) Notes on Algebraic Calculi of Processes, INRIA Rapports de Recherche 395.Google Scholar
Boudol, G. and Castellani, I. (1987) On the Semantics of Concurrency: Partial Orders and Transition Systems. In: Proceedings TAPSOFT ‘87. Springer-Verlag LNCS 249 123–137.Google Scholar
Brinch Hansen, P. (1987) On Concurrent Programs, unpublished lecture notes, Syracuse University.Google Scholar
Castellani, I. and Hennessy, M. (1989) Distributed Bisimulations. J.ACM 36 887–911.CrossRefGoogle Scholar
Degano, P. and Montanari, U. (1987) Concurrent Histories: a Basis for Observing Distributed Systems. J. Comput. Sys. Sci. 34 442–61.CrossRefGoogle Scholar
Devillers, R. (1991) Maximality Preservation and the ST-idea for Action Refinements, Technical Report LIT-242, Universite Libre de Bruxelles.CrossRefGoogle Scholar
Elgot, C. and Shepherdson, J. (1979) A Semantically Meaningful Characterization of Reducible Flowchart Schemes. Theoretical Comp. Sci. 8 325–357.CrossRefGoogle Scholar
Gischer, J. (1984) Partial Orders and the Axiomatic Theory of Shuffle, Ph.D. Thesis, Computer Science Dept., Stanford University.Google Scholar
van Glabbeek, R. and Goltz, U. (1990a) Refinement of Actions in Causality Based Models. In: De Bakker, J. W., de Roever, W.-P. and Rozenberg, G. (eds.), Stepwise Refinement of Distributed Systems: Models, Formalism, Correctness, Proceedings REX Workshop, Mook, The Netherlands, May/June 1989. Springer-Verlag LNCS 430 267–300.Google Scholar
van Glabbeek, R. and Goltz, U. (1990b) Equivalences and Refinement. In: Guessarian, I. (ed.), Semantics of Systems of Concurrent Processes, Proceedings LITP Spring School on Theoretical Computer Science, La Roche-Posay, France, April 1990. Springer-Verlag LNCS 469 309–333.Google Scholar
van Glabbeek, R. and Vaandrager, F. (1987) Petri Net Models for Algebraic Theories of Concurrency, PARLE. Springer-Verlag LNCS 259 224–242.Google Scholar
Goltz, U. (1990) CCS and Petri Nets. Arbeitspapiere der GMD 467.Google Scholar
Goltz, U. and Mycroft, A. (1984) On the Relationship of CCS and Petri Nets. In: Jan, Paredaens (ed.), Proceedings ICALP ‘84. Springer-Verlag LNCS 172.Google Scholar
Hoare, C. A. R. (1978) Communicating Sequential Processes. Comm. ACM 21 666–677.CrossRefGoogle Scholar
Hoare, C. A. R. (1980) A Model for Communicating Sequential Processes. In: McKeag, and Macnaghten, (eds.), On the Construction of Programs, Cambridge University Press.Google Scholar
Hoare, C. A. R. (1985) Communicating Sequential Processes, Prentice Hall.Google Scholar
Milne, G. (1985) CIRCAL and the Representation of Communication, Concurrency, and Time. Trans. Prog. Lang. Syst. 7 270–298.CrossRefGoogle Scholar
Milner, R. (1980) A Calculus of Communicating Systems. Springer-Verlag LNCS 92.Google Scholar
Milner, R. (1982) Four Combinators for Concurrency. ACM Principles of Distributed Computing 104–110.CrossRefGoogle Scholar
Milner, R. (1984) A Complete Inference System for a Class of Regular behaviours. J. Comput. System Sci. 28 439–466.CrossRefGoogle Scholar
Murphy, D. (1990) Timed Process Algebra, Petri Nets, and Event Refinement. In: Morris, J. (ed.), Refinement, Springer,.Google Scholar
Nielson, M., Plotkin, G. and Winskel, G. (1981) Petri Nets, Event Structures and Domains, Part I. Theor. Comp. Sci. 13 85–108.CrossRefGoogle Scholar
Nielson, M. and Thiagarajan, P.S.. (1984) Degrees of Non-Determinism and Concurrency: A Petri-Net View. In: Joseph, M. and Shyamasundar, R. (eds.), Proc. of the 5th Conf. on Found, of Softw. Techn. and Theor. Comp. Sci. Springer-Verlag LNCS 181 89–118.Google Scholar
Olderog, E. ( 1987) Operational Petri Net Semantics for CCSP. In: Rozenberg, G. (ed.), Advances in Petri Nets, 1987. Springer-Verlag LNCS 266.Google Scholar
Olderog, E. (1989) Strong Bisimilarity on Nets: a New Concept for Comparing Net Semantics, Linear Time, Branching Time, and Partial Order in Logics and Models for Concurrency. Springer-Verlag LNCS 354.Google Scholar
Olderog, E. (1991) Nets, Terms, and Formulas. Cambridge Tracts in Theoretical Computer Science 23, Cambridge University Press.Google Scholar
Olderog, E.Goltz, U. and van Glabbeek, R. (1988) Summary of a Workshop on Combining Compositionality and Concurrency. Arbeitspapiere der GMD 320.Google Scholar
Park, D.M.R. (1981) Concurrency and Automata on Infinite Sequences. In: Deussen, P. (ed.), Proc. 5th GI Conference. Springer-Verlag LNCS 104 167–183.Google Scholar
Pomello, L. (1986) Some Equivalence Notions for Concurrent Systems. In: Rozenberg, G. (ed.), Advances in Petri Nets, 1985. Springer-Verlag LNCS 222 381–400.Google Scholar
Pratt, V. R. (1986) Modelling Concurrency with Partial Orders. International Journal of Parallel Programming 15 33–71.CrossRefGoogle Scholar
Taubner, D. (1989) Finite Representations of CCS and TCSP Programs by Finite Automata and Petri Nets. Springer-Verlag LNCS 369.Google Scholar
Taubner, D. and Vogler, W. (1987) The Step Failure Semantics. In: Proc. STACS 87. Springer-Verlag LNCS 247 348–359.Google Scholar
Tindell, R. (1991) Covering Morphisms and Unique Minimal D-Schemes. Ada Cybernetica 10 101–112.Google Scholar
Vaandrager, F. (1991) Determinism → (Event Structure Isomorphism = Step Sequence Equivalence). Theoretical Computer Science 79 275–294.CrossRefGoogle Scholar
Wolfram, S. (1988) Mathematica, Addison Wesley.Google Scholar