Rainbow of Computer Science pp 90-101

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6570) | Cite as

Local Squares, Periodicity and Finite Automata

  • Mari Huova
  • Juhani Karhumäki
  • Aleksi Saarela
  • Kalle Saari


We consider the general problem when local regularity implies the global one in the setting where local regularity means the existence of a square of certain length in every position of an infinite word. The square can occur as centered or to the left or to the right from each position. In each case there are three variants of the problem depending on whether the square is that of words, that of abelian words or, as an in between case, that of so called k-abelian words. The above nine variants of the problem are completely solved, and some open problems are addressed in the k-abelian case. Finally, an amazing unavoidability result for 2-abelian squares is obtained.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Mari Huova
    • 1
  • Juhani Karhumäki
    • 1
  • Aleksi Saarela
    • 1
  • Kalle Saari
    • 1
  1. 1.Department of Mathematics and Turku Centre for Computer Science TUCSUniversity of TurkuTurkuFinland

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