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IFIP International Conference on Theoretical Computer Science

TCS 2012: Theoretical Computer Science pp 104–118Cite as

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A Context-Free Linear Ordering with an Undecidable First-Order Theory

A Context-Free Linear Ordering with an Undecidable First-Order Theory

  • Arnaud Carayol18 &
  • Zoltán Ésik19 
  • Conference paper
  • 796 Accesses

  • 1 Citations

  • 7 Altmetric

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7604)

Abstract

The words of a context-free language, ordered by the lexicographic ordering, form a context-free linear ordering. It is well-known that the linear orderings associated with deterministic context-free languages have a decidable monadic second-order theory. In stark contrast, we give an example of a context-free language whose lexicographic ordering has an undecidable first-order theory.

Keywords

  • Disjoint Union
  • Linear Ordering
  • Regular Language
  • Order Type
  • Countable Word

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Arnaud Carayol has been supported by the project AMIS (ANR 2010 JCJC 0203 01 AMIS). Both authors received partial support from the project TÁMOP-4.2.1/B-09/1/KONV-2010-0005 “Creating the Center of Excellence at the University of Szeged”, supported by the European Union and co-financed by the European Regional Fund. Zoltán Ésik was also partly supported by the National Foundation of Hungary for Scientific Research, grant no. K 75249, and by a chair Labex Bézout as part of the program “Investissements d’Avenir” (ANR-10-LABX-58).

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Author information

Authors and Affiliations

  1. Laboratoire d’Informatique Gaspard-Monge, Université Paris-Est, France

    Arnaud Carayol

  2. Institute of Informatics, University of Szeged, Hungary

    Zoltán Ésik

Authors
  1. Arnaud Carayol
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  2. Zoltán Ésik
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Editor information

Editors and Affiliations

  1. Centrum Wiskunde & Informatica (CWI), Science Park 123, 1098 XG, Amsterdam, The Netherlands

    Jos C. M. Baeten & Frank S. de Boer & 

  2. Microsoft Research, One Microsoft Way, 98052, Redmond, WA, USA

    Tom Ball

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© 2012 IFIP International Federation for Information Processing

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Cite this paper

Carayol, A., Ésik, Z. (2012). A Context-Free Linear Ordering with an Undecidable First-Order Theory. In: Baeten, J.C.M., Ball, T., de Boer, F.S. (eds) Theoretical Computer Science. TCS 2012. Lecture Notes in Computer Science, vol 7604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33475-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-33475-7_8

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  • Print ISBN: 978-3-642-33474-0

  • Online ISBN: 978-3-642-33475-7

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