Regular and context-free pattern languages over small alphabets

  • Authors:
  • Daniel Reidenbach;Markus L. Schmid

  • Affiliations:
  • Department of Computer Science, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom;Fachbereich 4 - Abteilung Informatik, Universität Trier, D-54296 Trier, Germany

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2014

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Abstract

Pattern languages are generalisations of the copy language, which is a standard textbook example of a context-sensitive and non-context-free language. In this work, we investigate a counter-intuitive phenomenon: with respect to alphabets of size 2 and 3, pattern languages can be regular or context-free in an unexpected way. For this regularity and context-freeness of pattern languages, we give several sufficient and necessary conditions and improve known results.