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Binary Patterns in Infinite Binary Words

  • Antonio Restivo
  • Sergio Salemi
Chapter
Part of the Lecture Notes in Computer Science book series (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.

Keywords

Pattern Complexity Injective Morphism Binary Word Binary Alphabet Standard Word 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Antonio Restivo
    • 1
  • Sergio Salemi
    • 1
  1. 1.Dipartimento di Matematica ed ApplicazioniUniversity of PalermoPalermoItaly

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