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Formal and Natural Computing pp 107–116Cite as

Binary Patterns in Infinite Binary Words

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2300))

Abstract

In this paper we study the set P(ω) of binary patterns that can occur in one infinite binary word ω, comparing it with the set F(ω) of factors of the word. Since the set P(ω) can be considered as an extension of the set F(ω), we first investigate how large is such extension, by introducing the parameter △(ω) that corresponds to the cardinality of the difference set P(ω) / F(ω). Some non trivial results about such parameter are obtained in the case of the Thue-Morse and the Fibonacci words. Since, in most cases, the parameter △(ω) is infinite, we introduce the pattern complexity of ω, which corresponds to the complexity of the language P(ω). As a main result, we prove that there exist infinite words that have pattern complexity that grows more quickly than their complexity. We finally propose some problems and new research directions.

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. Computer Science Department, Technical University of Munich, Arcisstraße 21, 80333, Munich, Germany

    Wilfried Brauer

  2. Computer Science Department, Technical University of Berlin, Franklinstraße 28/29, 10587, Berlin, Germany

    Hartmut Ehrig

  3. Department of Mathematics, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  4. Turku Centre for Computer Science, Lemminkäisenkatu 14A, 20520, Turku, Finland

    Arto Salomaa

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Restivo, A., Salemi, S. (2002). Binary Patterns in Infinite Binary Words. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds) Formal and Natural Computing. Lecture Notes in Computer Science, vol 2300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45711-9_8

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  • DOI: https://doi.org/10.1007/3-540-45711-9_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43190-9

  • Online ISBN: 978-3-540-45711-4

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