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Title: Existence and nonexistence of descriptive patterns
Authors: Freydenberger, Dominik D.
Reidenbach, Daniel
Keywords: Pattern languages
Descriptive patterns
Issue Date: 2010
Publisher: © Elsevier
Citation: FREYDENBERGER, D.D. and REIDENBACH, D., 2010. Existence and nonexistence of descriptive patterns. Theoretical Computer Science, 411 (34-36), pp. 3274-3286.
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 to 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 et al. (Pattern languages with and without erasing, 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.
Description: This article was published in the journal, Theoretical Computer Science [© Elsevier] and the definitive version is available at: www.elsevier.com/locate/tcs
Version: Accepted for publication
DOI: 10.1016/j.tcs.2010.05.033
URI: https://dspace.lboro.ac.uk/2134/6459
ISSN: 0304-3975
Appears in Collections:Published Articles (Computer Science)

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