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International Conference on Foundations of Software Technology and Theoretical Computer Science

FSTTCS 2003: FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science pp 112–123Cite as

The Caucal Hierarchy of Infinite Graphs in Terms of Logic and Higher-Order Pushdown Automata

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2914))

Abstract

In this paper we give two equivalent characterizations of the Caucal hierarchy, a hierarchy of infinite graphs with a decidable monadic second-order (MSO) theory. It is obtained by iterating the graph transformations of unfolding and inverse rational mapping. The first characterization sticks to this hierarchical approach, replacing the language-theoretic operation of a rational mapping by an MSO-transduction and the unfolding by the treegraph operation. The second characterization is non-iterative. We show that the family of graphs of the Caucal hierarchy coincides with the family of graphs obtained as the ε-closure of configuration graphs of higher-order pushdown automata.

While the different characterizations of the graph family show their robustness and thus also their importance, the characterization in terms of higher-order pushdown automata additionally yields that the graph hierarchy is indeed strict.

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Author information

Authors and Affiliations

  1. IRISA Rennes, France

    Arnaud Carayol

  2. Lehrstuhl für Informatik 7, RWTH Aachen, Germany

    Stefan Wöhrle

Authors
  1. Arnaud Carayol
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  2. Stefan Wöhrle
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Editor information

Editors and Affiliations

  1. Tata Institute of Fundamental Research, India

    Paritosh K. Pandya

  2. Tata Institute of Fundamental Research, School of Technology and Computer Science, Mumbai, India

    Jaikumar Radhakrishnan

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Carayol, A., Wöhrle, S. (2003). The Caucal Hierarchy of Infinite Graphs in Terms of Logic and Higher-Order Pushdown Automata. In: Pandya, P.K., Radhakrishnan, J. (eds) FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2003. Lecture Notes in Computer Science, vol 2914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24597-1_10

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  • DOI: https://doi.org/10.1007/978-3-540-24597-1_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20680-4

  • Online ISBN: 978-3-540-24597-1

  • eBook Packages: Springer Book Archive

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