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Inclusion Problems for Patterns with a Bounded Number of Variables

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Developments in Language Theory (DLT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6224))

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Abstract

We study the inclusion problems for pattern languages that are generated by patterns with a bounded number of variables. This continues the work by Freydenberger and Reidenbach (Information and Computation 208 (2010)) by showing that restricting the inclusion problem to significantly more restricted classes of patterns preserves undecidability, at least for comparatively large bounds. For smaller bounds, we prove the existence of classes of patterns with complicated inclusion relations, and an open inclusion problem, that are related to the Collatz Conjecture. In addition to this, we give the first proof of the undecidability of the inclusion problem for NE-pattern languages that, in contrast to previous proofs, does not rely on the inclusion problem for E-pattern languages, and proves the undecidability of the inclusion problem for NE-pattern languages over binary and ternary alphabets.

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Authors and Affiliations

  1. Institut für Informatik, Goethe Universität, Frankfurt am Main, Germany

    Joachim Bremer & Dominik D. Freydenberger

Authors
  1. Joachim Bremer
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  2. Dominik D. Freydenberger
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science, University of Western Ontario, N6A 5B7, London, ON, Canada

    Yuan Gao , Hanlin Lu , Shinnosuke Seki  & Sheng Yu , ,  & 

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Bremer, J., Freydenberger, D.D. (2010). Inclusion Problems for Patterns with a Bounded Number of Variables. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds) Developments in Language Theory. DLT 2010. Lecture Notes in Computer Science, vol 6224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14455-4_11

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  • DOI: https://doi.org/10.1007/978-3-642-14455-4_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14454-7

  • Online ISBN: 978-3-642-14455-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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