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Bad News on Decision Problems for Patterns

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Developments in Language Theory (DLT 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5257))

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Abstract

We study the inclusion problem for pattern languages, which is shown to be undecidable by Jiang et al. (J. Comput. System Sci. 50, 1995). More precisely, Jiang et al. demonstrate that there is no effective procedure deciding the inclusion for the class of all pattern languages over all alphabets. Most applications of pattern languages, however, consider classes over fixed alphabets, and therefore it is practically more relevant to ask for the existence of alphabet-specific decision procedures. Our first main result states that, for all but very particular cases, this version of the inclusion problem is also undecidable. The second main part of our paper disproves the prevalent conjecture on the inclusion of so-called similar E-pattern languages, and it explains the devastating consequences of this result for the intensive previous research on the most prominent open decision problem for pattern languages, namely the equivalence problem for general E-pattern languages.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Goethe-Universität, Postfach 111932, D-60054, Frankfurt am Main, Germany

    Dominik D. Freydenberger

  2. Department of Computer Science, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom

    Daniel Reidenbach

Authors
  1. Dominik D. Freydenberger
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  2. Daniel Reidenbach
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Editor information

Masami Ito Masafumi Toyama

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Freydenberger, D.D., Reidenbach, D. (2008). Bad News on Decision Problems for Patterns. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2008. Lecture Notes in Computer Science, vol 5257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85780-8_26

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  • DOI: https://doi.org/10.1007/978-3-540-85780-8_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85779-2

  • Online ISBN: 978-3-540-85780-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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