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An algebraic theory of graph reduction

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Graph Grammars and Their Application to Computer Science (Graph Grammars 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 532))

Abstract

We show how membership in classes of graphs definable in monadic second order logic and of bounded treewidth can be decided by finite sets of terminating reduction rules. The method is constructive in the sense that we describe an algorithm which will produce, from a formula in monadic second order logic and an integer k such that the class defined by the formula is of treewidth ≤ k, a set of rewrite rules that reduces any member of the class to one of finitely many graphs, in a number of steps bounded by the size of the graph. This reduction system corresponds to an algorithm that runs in time linear in the size of the graph.

Supported by NFR and STU.

Supported by the ”Programme de Recherches Coordonnées: Mathematiques et Informatique” and the ESPRIT-BRA project 3299 ”Computing by Graph Transformations”.

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Author information

Authors and Affiliations

  1. The Royal Institute of Technology NADA, KTH, S-100 44, Stockholm, Sweden

    Stefan Arnborg

  2. Laboratorie d'Informatique (associé au CNRS), Bordeaux-1 University, 351 cours de la Libération, 33405, Talence, France

    Bruno Courcelle

  3. CIS department, University of Oregon, 97403, Eugene, Oregon, USA

    Andrzej Proskurowski

  4. Akademie der Wissenschaften, Karl-Weierstraß Institute für Mathematik, Mohrenstr. 39, PF 1304, 1086, Berlin, Germany

    Detlef Seese

Authors
  1. Stefan Arnborg
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  2. Bruno Courcelle
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  3. Andrzej Proskurowski
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  4. Detlef Seese
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Editor information

Hartmut Ehrig Hans-Jörg Kreowski Grzegorz Rozenberg

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© 1991 Springer-Verlag Berlin Heidelberg

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Arnborg, S., Courcelle, B., Proskurowski, A., Seese, D. (1991). An algebraic theory of graph reduction. In: Ehrig, H., Kreowski, HJ., Rozenberg, G. (eds) Graph Grammars and Their Application to Computer Science. Graph Grammars 1990. Lecture Notes in Computer Science, vol 532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017382

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  • DOI: https://doi.org/10.1007/BFb0017382

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54478-4

  • Online ISBN: 978-3-540-38395-6

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