Existence and Nonexistence of Descriptive Patterns

  • Dominik D. Freydenberger
  • Daniel Reidenbach
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5583)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

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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