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Linear Orders in the Pushdown Hierarchy

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Automata, Languages and Programming (ICALP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6199))

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Abstract

We investigate the linear orders belonging to the pushdown hierarchy. Our results are based on the characterization of the pushdown hierarchy by graph transformations due to Caucal and do not make any use of higher-order pushdown automata machinery.

Our main results show that ordinals belonging to the n-th level are exactly those strictly smaller than the tower of ω of height n + 1. More generally the Hausdorff rank of scattered linear orders on the n-th level is strictly smaller than the tower of ω of height n. As a corollary the Cantor-Bendixson rank of the tree solutions of safe recursion schemes of order n is smaller than the tower of ω of height n.

As a spin-off result, we show that the ω-words belonging to the second level of the pushdown hierarchy are exactly the morphic words.

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Authors and Affiliations

  1. LIGM, Université Paris-Est & CNRS,  

    Laurent Braud & Arnaud Carayol

Authors
  1. Laurent Braud
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  2. Arnaud Carayol
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Editor information

Editors and Affiliations

  1. Computing Laboratory, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Samson Abramsky

  2. Université de Bordeaux (LaBRI) & INRIA, 351, cours de la Libération, 33405, Talence Cedex, France,

    Cyril Gavoille

  3. INRIA, Centre de Recherche Bordeaux – Sud-Ouest, 351 cours de la Libération, 33405, Talence Cedex, France

    Claude Kirchner

  4. Heinz Nixdorf Institute, University of Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Friedhelm Meyer auf der Heide

  5. University of Patras and RACTI, 26500, Patras, Greece

    Paul G. Spirakis

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Braud, L., Carayol, A. (2010). Linear Orders in the Pushdown Hierarchy. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14162-1_8

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  • DOI: https://doi.org/10.1007/978-3-642-14162-1_8

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  • Print ISBN: 978-3-642-14161-4

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