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Pullback as a Generic Graph Rewriting Mechanism

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Abstract

Rewriting usually relies on a notion of substitution which can be understood as the succession of three basic operations: deletion of the part to be rewritten to provide a context, union of this context with the right-hand side of a rule, liaison of those two parts, most often by identification of some corresponding items.

In the field of graph rewriting, this has led to the elegant, productive and therefore popular method known as the double push-out approach to graph rewriting. Yet this method has met its descriptive limits when trying to deal with the various notions of node replacement.

In this paper we show how – when set in a proper framework – products (or pullbacks) can provide a very generic and uniform rewriting mechanism which extends uniformly to arbitrary complicated graph-like structures.

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Authors and Affiliations

  1. Laboratoire Bordelais de Recherche en Informatique, Unité Mixte de Recherche CNRS 5800, Université Bordeaux I, F-33405, Talence Cedex, France

    Michel Bauderon

  2. France

    Hélène Jacquet

Authors
  1. Michel Bauderon
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  2. Hélène Jacquet
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Bauderon, M., Jacquet, H. Pullback as a Generic Graph Rewriting Mechanism. Applied Categorical Structures 9, 65–82 (2001). https://doi.org/10.1023/A:1008610714027

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