Inclusion Problems for Patterns with a Bounded Number of Variables

  • Joachim Bremer
  • Dominik D. Freydenberger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6224)


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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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Joachim Bremer
    • 1
  • Dominik D. Freydenberger
    • 1
  1. 1.Institut für InformatikGoethe UniversitätFrankfurt am MainGermany

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