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On relating rewriting systems and graph grammars to event structures

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Graph Transformations in Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 776))

Abstract

In this paper, we investigate how rewriting systems and especially graph grammars as operational models of parallel and distributed systems can be related to event structures as more abstract models. First, distributed rewriting systems that are based on the notion of contexts are introduced as a common framework for different kinds of rewriting systems and their parallelism properties are investigated. Then we introduce concrete graph grammars and show how they can be integrated into this framework for rewriting systems. A construction for the Mazurkiewicz trace language related to the derivation sequences of a distributed rewriting system is presented. Since there is a well-known relation between trace languages and event structures, this provides the link between (graph) rewriting and event structures.

Supported in part by Deutsche Forschungsgemeinschaft (SFB 182, B1)

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References

  1. M. Bauderon and B. Courcelle. Graph expressions and graph rewritings. Math. Systems Theory, 20:83–127, 1987.

    Article  Google Scholar 

  2. M.A. Bednarczyk. Categories of asynchronous systems. PhD thesis, University of Sussex, 1987.

    Google Scholar 

  3. A. Corradini, H. Ehrig, M. Löwe, U. Montanari, and F. Rossi. True concurrency in graph grammars. In Dagstuhl Seminar-Report, number 9301, pages 12–13, 1993.

    Google Scholar 

  4. A. Corradini and U. Montanari. An algebra of graphs and graph rewriting. Lecture Notes in Computer Science 530, Springer, 1991.

    Google Scholar 

  5. P. Degano and U. Montanari. A model for distributed systems based on graph rewriting. Journal of the ACM, 34(2):411–449, 1987.

    Google Scholar 

  6. H. Ehrig. Introduction to the algebraic theory of graph grammars (a survey). Lecture Notes in Computer Science 73, pages 1–69, Springer, 1979.

    Google Scholar 

  7. A. Habel and H.-J. Kreowski. May we introduce to you: Hyperedge replacement. Lecture Notes in Computer Science 291, Springer, pages 15–25, 1987.

    Google Scholar 

  8. D. Janssens and G. Rozenberg. Actor grammars. Mathematical Systems Theory, 22:75–107, 1989.

    Google Scholar 

  9. R. Kennaway. Private communication. January, 1993.

    Google Scholar 

  10. A. Mazurkiewicz. Trace theory. Lecture Notes in Computer Science 255, pages 279–323. Springer-Verlag, 1987.

    Google Scholar 

  11. J. Meseguer. Rewriting as a unified model of concurrency. Technical Report SRI-CSL-90-02R, SRI International, Computer Science Laboratory, 1990.

    Google Scholar 

  12. M. Nielsen, G. Plotkin, and G. Winskel. Petri nets, event structures and domains. Theoretical Computer Science, 13:85–108, 1981.

    Article  Google Scholar 

  13. J.C. Raoult. On graph rewritings. Theoretical Computer Science, 32:1–24, 1984.

    Google Scholar 

  14. H.J. Schneider. Describing distributed systems by categorical graph grammars. Lecture Notes in Computer Science 411, pages 121–135. Springer, 1990.

    Google Scholar 

  15. G. Schied. Über Graphgrammatiken, eine Spezifikationsmethode für Programmiersprachen und verteilte Regelsysteme. Arbeitsberichte des IMMD, Band 25, Nr. 2, Universität Erlangen-Nürnberg, 1992.

    Google Scholar 

  16. E.W. Stark. Concurrent transition systems. Theoretical Computer Science, 64:221–269, 1989.

    Google Scholar 

  17. E. W. Stark. Connections between a concrete and an abstract model of concurrent systems. Lecture Notes in Computer Science 442, pages 53–79. Springer, 1990.

    Google Scholar 

  18. G. Winskel. An introduction to event structures. Lecture Notes in Computer Science 354, pages 364–397, Springer, 1989.

    Google Scholar 

  19. G. Winskel. Categories of models for concurrency. Advanced School on the Algebraic Logical and Categorical Foundations of Concurrency, Gargnano del Garda, Italy, 1991.

    Google Scholar 

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Hans Jürgen Schneider Hartmut Ehrig

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© 1994 Springer-Verlag Berlin Heidelberg

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Schied, G. (1994). On relating rewriting systems and graph grammars to event structures. In: Schneider, H.J., Ehrig, H. (eds) Graph Transformations in Computer Science. Lecture Notes in Computer Science, vol 776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57787-4_21

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  • DOI: https://doi.org/10.1007/3-540-57787-4_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57787-4

  • Online ISBN: 978-3-540-48333-5

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