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Bisimulation Equivalences for Graph Grammars

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Formal and Natural Computing

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2300))

Abstract

Along the years the concurrent behaviour of graph grammars has been widely investigated, and, in particular, several classical approaches to the semantics of Petri nets have been extended to graph grammars. Most of the existing semantics for graph grammars provide a (possibly concurrent) operational model of computation, while little interest has been devoted to the definition of abstract observational semantics. The aim of this paper is to introduce and study a behavioural equivalence over graphg rammars, inspired by the classical history preserving bisimulation. Several choices are conceivable according to the kind of concurrent observation one is interested in. We concentrate on the basic case where the concurrent nature of a graph grammar computation is described by means of a prime event structure. As it happens for Petri nets, history preserving bisimulation can be studied in the general framework of causal automata — a variation of ordinary automata introduced to deal withh istory dependent formalisms. In particular, we prove that history preserving bisimulation is decidable for finite-state graph grammars, by showing how the problem can be reduced to deciding the equivalence of finite causal automata.

Research partially supported by the EC TMR Network GETGRATS, by the ESPRIT Working Group APPLIGRAPH and by the MURST project TOSCA.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Corso Italia, 40, 56125, Pisa, Italy

    Paolo Baldan, Andrea Corradini & Ugo Montanari

Authors
  1. Paolo Baldan
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  2. Andrea Corradini
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  3. Ugo Montanari
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Editor information

Editors and Affiliations

  1. Computer Science Department, Technical University of Munich, Arcisstraße 21, 80333, Munich, Germany

    Wilfried Brauer

  2. Computer Science Department, Technical University of Berlin, Franklinstraße 28/29, 10587, Berlin, Germany

    Hartmut Ehrig

  3. Department of Mathematics, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  4. Turku Centre for Computer Science, Lemminkäisenkatu 14A, 20520, Turku, Finland

    Arto Salomaa

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Baldan, P., Corradini, A., Montanari, U. (2002). Bisimulation Equivalences for Graph Grammars. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds) Formal and Natural Computing. Lecture Notes in Computer Science, vol 2300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45711-9_11

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  • DOI: https://doi.org/10.1007/3-540-45711-9_11

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  • Print ISBN: 978-3-540-43190-9

  • Online ISBN: 978-3-540-45711-4

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