Existence and Nonexistence of Descriptive Patterns

  • Authors:

  • Dominik D. Freydenberger;Daniel Reidenbach

  • Affiliations:

  • Institut für Informatik, Goethe-Universität, Frankfurt am Main, Germany D-60054;Department of Computer Science, Loughborough University, Loughborough, United Kingdom LE11 3TU

  • Venue:
  • DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
  • Year:
  • 2009

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Abstract

In the present paper, we study the existence of descriptive patterns, i. e. patterns that cover all words in a given set through morphisms and that are optimal in terms of revealing commonalities of these words. Our main result shows that if patterns may be mapped onto words by arbitrary morphisms, then there exist infinite sets of words that do not have a descriptive pattern. This answers a question posed by Jiang, Kinber, Salomaa, Salomaa and Yu (International Journal of Computer Mathematics 50, 1994). Since the problem of whether a pattern is descriptive depends on the inclusion relation of so-called pattern languages, our technical considerations lead to a number of deep insights into the inclusion problem for and the topology of the class of terminal-free E-pattern languages.