On complexity functions of infinite words associated with generalized Dyck languages

  • Authors:
  • Marion Le Gonidec

  • Affiliations:
  • Institut de Mathématiques de lUniversité de Liège, Grande traverse 12, Bat B37, B-4000 Liège, Belgique

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2008

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Abstract

In this article, we construct a family of infinite words, generated by countable automata and also generated by substitutions over infinite alphabets, closely related to parenthesis languages and we study their complexity functions. We obtain a family of binary infinite words m^(^b^), indexed on the number b=1 of parenthesis types, such that the growth order of the complexity function of m^(^b^) is n(logn)^2 if b=1 and n^1^+^l^o^g^"^2^"^b^b if b=2.