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Branch-Width, Parse Trees, and Monadic Second-Order Logic for Matroids

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STACS 2003 (STACS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2607))

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Abstract

We introduce “matroid parse trees” which, using only a limited amount of information, can build up all matroids of bounded branchwidth representable over a finite field. We prove that if M is a family of matroids described by a sentence in the second-order monadic logic of matroids, then the parse trees of bounded-width representable members of M can be recognized by a finite tree automaton. Since the cycle matroids of graphs are representable over any finite field, our result directly extends the well-known “MS 2-theorem” for graphs of bounded tree-width by Courcelle and others. This work has algorithmic applications in matroid or coding theories.

This work is based on an original research that the author carried out at the Victoria University of Wellington in New Zealand, supported by a Marsden Fund research grant to Geo. Whittle.

ITI is supported by Ministry of Education of Czech Republic as project LN00A056.

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Comp. Science (IMI SAV), Matej Bel University, Severná ulica 5, 974 00, Banská Bystrica, Slovakia

    Petr Hliněný

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  1. Petr Hliněný
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Editors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takusstr. 9, 14195, Berlin, Germany

    Helmut Alt

  2. LIRMM, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Michel Habib

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Hliněný, P. (2003). Branch-Width, Parse Trees, and Monadic Second-Order Logic for Matroids. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_29

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  • DOI: https://doi.org/10.1007/3-540-36494-3_29

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00623-7

  • Online ISBN: 978-3-540-36494-8

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