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Words and Patterns

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Developments in Language Theory (DLT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2295))

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Abstract

In this paper some new ideas, problems and results on patterns are proposed. In particular, motivated by questions concerning avoidability, we first study the set of binary patterns that can occur in one infinite binary word, comparing it with the set of factors of the word. This suggests a classification of infinite words in terms of the “difference” between the set of its patterns and the set of its factors. The fact that each factor in an infinite word can give rise to several distinct patterns leads to study the set of patterns of a single finite word. This set, endowed with a natural order relation, defines a poset: we investigate the relationships between the structure of such a poset and the combinatorial properties of the word. Finally we show that the set of patterns of the words in a regular language is a regular language too.

Partially supported by MURST projects: Bioinformatica e Ricerca Genomica

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Authors and Affiliations

  1. Dipartimento di Matematica ed Applicazioni, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy

    Antonio Restivo & Sergio Salemi

Authors
  1. Antonio Restivo
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  2. Sergio Salemi
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Editor information

Editors and Affiliations

  1. Institut für Algebra und Computermathematik Abt. für Theoretische Informatik, Technische Universität Wien, Wiedner Hauptstraße 8-10, 1040, Wien, Austria

    Werner Kuich

  2. Department of Computer Science, Leiden University, P.O. Box 9512, 2300, RA Leiden, The Netherlands

    Grzegorz Rozenberg

  3. Turku Centre for Computer Science, Lemminkaisenkatu 14A, 20520, Turku, Finland

    Arto Salomaa

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© 2002 Springer-Verlag Berlin Heidelberg

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Restivo, A., Salemi, S. (2002). Words and Patterns. In: Kuich, W., Rozenberg, G., Salomaa, A. (eds) Developments in Language Theory. DLT 2001. Lecture Notes in Computer Science, vol 2295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46011-X_9

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  • DOI: https://doi.org/10.1007/3-540-46011-X_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43453-5

  • Online ISBN: 978-3-540-46011-4

  • eBook Packages: Springer Book Archive

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