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Monadic second-order definable graph transductions

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CAAP '92 (CAAP 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 581))

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Abstract

Formulas of monadic second-order logic can be used to specify graph transductions, i.e., multivalued functions from graphs to graphs. We obtain in this way classes of graph transductions, called monadic second-order definable graph transductions (or more simply definable transductions) that are closed under composition and preserve the two known classes of context-free sets of graphs, namely the class of Hyperedge Replacement (HR) and the class of Vertex Replacement (VR) sets. These two classes can be characterized in terms of definable transductions and recognizable sets of finite trees. These characterizations are independent of the rewriting mechanisms used to define the HR and VR grammars. When restricted to words, the definable transductions are strictly more powerful than the rational transductions with finite image; they do not preserve context-free languages. We also describe the sets of discrete (edgeless) labeled graphs that are the images of HR and VR sets under definable transductions: this gives a version of Parikh's Theorem (i.e., the characterization of the commutative images of context-free languages) which extends the classical one and applies to HR and VR sets of graphs.

Supported by the ESPRIT Basic -Research project 3299 (“Computing by graph transformations”) and by the “Programme de Recherches Coordonnées: Mathématiques et Informatique”.

Unité associée au CNRS n∘ 1304,

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Authors and Affiliations

  1. Laboratoire d'Informatique 351, Université Bordeaux-1, Cours de la Libération, 33405, Talence, France

    Bruno Courcelle

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  1. Bruno Courcelle
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J. -C. Raoult

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© 1992 Springer-Verlag Berlin Heidelberg

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Courcelle, B. (1992). Monadic second-order definable graph transductions. In: Raoult, J.C. (eds) CAAP '92. CAAP 1992. Lecture Notes in Computer Science, vol 581. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55251-0_7

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  • DOI: https://doi.org/10.1007/3-540-55251-0_7

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  • Print ISBN: 978-3-540-55251-2

  • Online ISBN: 978-3-540-46799-1

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