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Bad news on decision problems for patterns

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journal contribution
posted on 04.12.2009, 10:31 by Dominik FreydenbergerDominik Freydenberger, Daniel ReidenbachDaniel Reidenbach
We study the inclusion problem for pattern languages, which - due to Jiang et al. (Journal of Computer and System Sciences 50, 1995) - is known to be undecidable. 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.

History

School

  • Science

Department

  • Computer Science

Citation

FREYDENBERGER, D.D. and REIDENBACH, D., 2010. Bad news on decision problems for patterns. Information and Computation, 208 (1), pp. 83-96.

Publisher

© Elsevier

Version

AM (Accepted Manuscript)

Publication date

2010

Notes

This article was published in the journal, Information and Computation [© Elsevier] and the definitive version is available at: www.elsevier.com/locate/ic

ISSN

0890-5401

Language

en

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