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Prefix Rewriting for Nested-Words and Collapsible Pushdown Automata

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Automata, Languages, and Programming (ICALP 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7392))

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Abstract

We introduce two natural variants of prefix rewriting on nested-words. One captures precisely the transition graphs of order-2 pushdown automata and the other precisely those of order-2 collapsible pushdown automata (2-CPDA). To our knowledge this is the first precise ‘external’ characterisation of 2-CPDA graphs and demonstrates that the class is robust and hence interesting in its own right. The comparison with our characterisation for 2-PDA graphs also gives an idea of what ‘collapse means’ in terms outside of higher-order automata theory. Additionally, a related construction gives us a decidability result for first-order logic on a natural subclass of 3-CPDA graphs, which in some sense is optimal.

Supported by La Fondation Sciences Mathématiques de Paris and by the project AMIS (ANR 2010 JCJC 0203 01 AMIS) Full version: mjolnir.cs.ox.ac.uk/~chrb/isophilic.pdf

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Author information

Authors and Affiliations

  1. LIAFA (CNRS and Paris 7), Paris, France

    Christopher Broadbent

Authors
  1. Christopher Broadbent
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Centre for Discrete Mathematics and its Applications, University of Warwick, Warwick, UK

    Artur Czumaj

  2. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Kurt Mehlhorn

  3. Computer Laboratory,, University of Cambridge, UK

    Andrew Pitts

  4. ETH Zurich, Switzerland

    Roger Wattenhofer

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Broadbent, C. (2012). Prefix Rewriting for Nested-Words and Collapsible Pushdown Automata. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31585-5_17

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  • DOI: https://doi.org/10.1007/978-3-642-31585-5_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31584-8

  • Online ISBN: 978-3-642-31585-5

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