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A survey of behaviour and equivalence preserving refinements of petri nets

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Advances in Petri Nets 1990 (ICATPN 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 483))

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Abstract

Results on refinements of places and transitions in Petri nets are surveyed. Such refinements may either transform a net to a refined net with the same behaviour, where behaviour often means safeness or liveness. Or they may transform semantically equivalent nets to refined nets which are semantically equivalent again. Here the semantics of a net is a description of the possible runs incorporating information on choices to a varying degree.

This work was partially supported by the ESPRIT Basic Research Action No. 3148 DEMON (Design Methods Based on Nets)

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References

  1. L. Aceto: Full abstractions for series-parallel pomsets. Technical Report 1/90, Dept. Comp. Sci. Univ. of Sussex, Brighton, 1990.

    Google Scholar 

  2. L. Aceto and M. Hennesy: Towards action-refinement in process algebras. Technical Report 3/88, Dept. Comp. Sci. Univ. of Sussex, Brighton, 1988.

    Google Scholar 

  3. B. Baumgarten: On internal and external characterizations of PT-net building block behaviour. In: G. Rozenberg, editor, Advances in Petri Nets 1988, Lect. Notes Comp. Sci. 340 (1988) 44–61.

    Google Scholar 

  4. G. Boudol and I. Castellani: On the semantics of concurrency: Partial orders and transition systems. In: H. Ehrig et al., editors, TAPSOFT 87, Vol. I, Lect. Notes Comp. Sci. 249 (1987) 123–137.

    Google Scholar 

  5. L. Bernardinello, F. de Cindio: A survey of basic net models and modular net classes. submitted to Advances in Petri Nets.

    Google Scholar 

  6. E. Best, R. Devillers, A. Kiehn, and L. Pomello: Fully concurrent bisimulation. Technical Report LIT-202, Univ. Bruxelles, 1989; to appear in Acta Informatica.

    Google Scholar 

  7. S.D. Brookes, C.A.R. Hoare, and A.W. Roscoe: A theory of communicating sequential processes. J. ACM 31 (1984) 560–599.

    Google Scholar 

  8. S.D. Brookes and A.W. Roscoe: An improved failures model for communicating processes. In: S.D. Brookes, A.W. Roscoe, and G. Winskel, editors, Seminar on Concurrency, Lect. Notes Comp. Sci. 197 (1984) 281–305.

    Google Scholar 

  9. L. Castellano, G. De Michelis, and L. Pomello: Concurrency vs. interleaving: An instructive example. Bull. EATCS 31 (1987) 12–15.

    Google Scholar 

  10. P. Degano, R. De Nicola, and U. Montanari: Partial orderings descriptions and observations of nondeterministic concurrent processes. In: J.W. de Bakker et al., editors, Proc. REX School / Workshop Linear Time, Branching Time and Partial Order in Logic and Models of Concurrency. Noordwijkerhout, 1988, Lect. Notes Comp. Sci. 354 (1989) 438–466

    Google Scholar 

  11. R. Devillers: On the definition of a bisimulation notion based on partial words. Petri Net Newsletter 29 (1988) 16–19.

    Google Scholar 

  12. R. Devillers: Maximality preserving bisimulation. Technical Report LIT-214, Univ. Bruxelles, 1990.

    Google Scholar 

  13. E.W. Dijkstra: Hierarchical ordering of sequential processes. Acta Informatica 1 (1971) 115–138.

    Google Scholar 

  14. J. Desel and A. Merceron: P/T-systems as abstractions of C/E-systems. In: G. Rozenberg, editor, Advances in Petri Nets 1989, Lect. Notes Comp. Sci. 424 (1990) 105–127.

    Google Scholar 

  15. J. Desel and A. Merceron: Vicinity respecting morphisms. In: Proc. 10th Int. Conf. Applications and Theory of Petri Nets, Bonn, 1989, 115–138; to appear in Advances in Petri Nets 1990.

    Google Scholar 

  16. P. Degano, J. Meseguer, and U. Montanari: Axiomatizing net computations and processes. In Proc. 4th Ann. Symp. Logic in Comp. Sci. LICS 89, Asilomar, USA, 1989, 175–185.

    Google Scholar 

  17. P.C. Fishburn: Intransitive indifference with unequal indifference intervals. J. Math. Psych. 7 (1970) 144–149.

    Google Scholar 

  18. R.J. v. Glabbeek and U. Goltz: Equivalence notions for concurrent systems and refinement of actions. In: A. Kreczmar and G. Mirkowska, editors, MFCS 89, Lect. Notes Comp. Sci. 379 (1989) 237–248.

    Google Scholar 

  19. R.J. v. Glabbeek and U. Goltz: Refinement of actions in causality based models. Technical report, Arbeitspapiere der GMD 428, 1990.

    Google Scholar 

  20. R.J. v. Glabbeek: The refinement theorem for ST-bisimulation semantics. In: M. Broy and C.B. Jones, editors, Proc. IFIP Working Conference on Programming Concepts and Methods, Sea of Galilee, Israel, 1990, to appear.

    Google Scholar 

  21. J. Grabowski: On partial languages. Fundamenta Informaticae IV.2 (1981) 428–498.

    Google Scholar 

  22. H.J. Genrich and E. Stankiewicz-Wiechno: A dictionary of some basic notions of net theory. In: W. Brauer, editor, Net Theory and Applications, Lect. Notes Comp. Sci. 84 (1980) 519–531.

    Google Scholar 

  23. R.J. v. Glabbeek and F. Vaandrager: Petri net models for algebraic theories of concurrency. In: J.W. de Bakker et al., editors, PARLE Vol. II, Lect. Notes Comp. Sci. 259 (1987) 224–242.

    Google Scholar 

  24. R.J. v. Glabbeek and W.P. Weijland: Refinement in branching time semantics. Technical Report CS-R8922, CWI, Amsterdam, 1989.

    Google Scholar 

  25. M. Hennessy: Axiomatising finite concurrent processes. Technical Report 4/87, Dept. Comp. Sci. Univ. of Sussex, Brighton, 1987.

    Google Scholar 

  26. A. Kiehn: A Structuring Mechanism for Petri Nets. PhD thesis, Technical Report TUM-I8902, Inst. Informatik, Techn. Univ. München, 1989.

    Google Scholar 

  27. A. Kiehn: Petri net systems and their closure properties. In: G. Rozenberg, editor, Advances in Petri Nets 1989, Lect. Notes Comp. Sci. 424 (1990) 306–328.

    Google Scholar 

  28. L. Lamport: On interprocess communication I. Distributed Comp. 1 (1986) 77–85.

    Google Scholar 

  29. A. Mazurkiewicz: Traces, histories, graphs: Instances of a process monoid. In: M.P. Chytil et al., editors, Proceeding of the 11th Symposium on Mathematical Foundations of Computer Science (MFCS), Lect. Notes Comp. Sci. 176 (1984) 115–133.

    Google Scholar 

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

    Google Scholar 

  31. J. Meseguer and U. Montanari: Petri nets are monoids: A new algebraic foundation for net theory. In: Proc. 3rd Ann. Symp. Logic in Comp. Sci. LICS 88, Edinburgh. IEEE Computer Soc. Press, Washington (1988) 155–164.

    Google Scholar 

  32. K. Müller: Constructable Petri nets. Elektr. Inf. Kybern. 21 (1985) 171–199.

    Google Scholar 

  33. M. Nielsen, U. Engberg, and K. Larsen: Partial order semantics for concurrency. In: J.W. de Bakker et al., editors, Proc. REX School / Workshop Linear Time, Branching Time and Partial Order in Logic and Models of Concurrency. Noordwijkerhout, 1988, Lect. Notes Comp. Sci. 354 (1989) 523–548.

    Google Scholar 

  34. M. Nielsen, G.D. Plotkin, and G. Winskel: Petri nets, event structures and domains I. Theor. Comput. Sci. 13 (1981) 85–108.

    Google Scholar 

  35. M. Nielsen, G. Rozenberg, and P.S. Thiagarajan: Elementary transition systems. Techn. Rep. 90-13, Univ. Leiden, 1990.

    Google Scholar 

  36. D. Park: Concurrency and automata on infinite sequences. In: P. Deussen, editor, Proc. 5th GI Conf. on Theoretical Comp. Sci., Lect. Notes Comp. Sci 104 (1981) 167–183.

    Google Scholar 

  37. L. Pomello: Some equivalence notions for concurrent systems — an overview. In: G. Rozenberg, editor, Advances in Petri Nets 85, Lect. Notes Comp. Sci. 222 (1986) 381–400.

    Google Scholar 

  38. V. Pratt: Modelling concurrency with partial orders. Int. J. Parallel Prog. 15 (1986) 33–71.

    Google Scholar 

  39. L. Pomello and C. Simone: A state transformation preorder over a class of EN-systems. In: Proc. 10th Int. Conf. Applications and Theory of Petri Nets, Bonn, 1989.

    Google Scholar 

  40. L. Pomello and C. Simone: Preorders of concurrent systems. Internal report, DSI, Milano, 1990.

    Google Scholar 

  41. L. Pomello and C. Simone: A survey of equivalence notions for net based systems. submitted to Advances in Petri Nets.

    Google Scholar 

  42. A. Rabinovich and B.A. Trakhtenbrot: Behaviour structures and nets. Fundamenta Informaticae 11 (1988) 357–404.

    Google Scholar 

  43. I. Suzuki and T. Murata: A method for stepwise refinement and abstraction of Petri nets. J. Comp. Sys. Sci. 27 (1983) 51–76.

    Google Scholar 

  44. R. Valette: Analysis of Petri nets by stepwise refinement. J. Comp. Sys. Sci. 18 (1979) 35–46.

    Google Scholar 

  45. W. Vogler: Behaviour preserving refinements of Petri nets. In: G. Tinhofer and G. Schmidt, editors, Graph-Theoretic Concepts in Computer Science, Proc. WG 86, Bernried, Lect. Notes Comp. Sci. 246 (1987) 82–93.

    Google Scholar 

  46. W. Vogler: Failures semantics and deadlocking of modular Petri nets. Acta Informatica 26 (1989) 333–348.

    Google Scholar 

  47. W. Vogler: Failures semantics based on interval semiwords is a congruence for refinement. In: C. Choffrut and T. Lengauer, editors, STACS 90, Lect. Notes Comp. Sci. 415 (1990) 285–297; to appear in Distributed Computing

    Google Scholar 

  48. W. Vogler: Failures semantics of Petri nets and the refinement of places and transitions. Technical Report TUM-I9003, Inst. Informatik, Techn. Univ. München, 1990.

    Google Scholar 

  49. W. Vogler: Bisimulation and action refinement. Technical Report SFB-Bericht Nr. 342/10/90A, Inst. Informatik, Techn. Univ. München, 1990.

    Google Scholar 

  50. G. Winskel: Petri nets, algebras, morphisms, and compositionality. Inform. and Computation 72 (1987) 197–238.

    Google Scholar 

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Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Arcisstr. 21, D-8000, München 2

    Wilfried Brauer, Robert Gold & Walter Vogler

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  1. Wilfried Brauer
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  2. Robert Gold
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  3. Walter Vogler
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Grzegorz Rozenberg

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Brauer, W., Gold, R., Vogler, W. (1991). A survey of behaviour and equivalence preserving refinements of petri nets. In: Rozenberg, G. (eds) Advances in Petri Nets 1990. ICATPN 1989. Lecture Notes in Computer Science, vol 483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53863-1_19

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  • DOI: https://doi.org/10.1007/3-540-53863-1_19

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  • Online ISBN: 978-3-540-46369-6

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