Bad News on Decision Problems for Patterns

  • Dominik D. Freydenberger
  • Daniel Reidenbach
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5257)


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.


Inductive Inference Equivalence Problem Inclusion Problem Pattern Language Alphabet Size 
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.


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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Dominik D. Freydenberger
    • 1
  • Daniel Reidenbach
    • 2
  1. 1.Institut für InformatikGoethe-UniversitätFrankfurt am MainGermany
  2. 2.Department of Computer ScienceLoughborough UniversityLoughboroughUnited Kingdom

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