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On Recognizing Words That Are Squares for the Shuffle Product

  • Romeo Rizzi
  • Stéphane Vialette
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7913)

Abstract

The shuffle of two words u and v of A * is the language u ш v consisting of all words u 1 v 1 u 2 v 2u k v k , where k ≥ 0 and the u i and the v i are the words of A * such that u = u 1 u 2u k and v = v 1 v 2v k . A word u ∈ A * is a square for the shuffle product if it is the shuffle of two identical words (i.e., u ∈ v ш v for some v ∈ A *). Whereas, it can be tested in polynomial-time whether or not u ∈ v 1 ш v 2 for given words u, v 1 and v 2 [J.-C. Spehner, Le Calcul Rapide des Mélanges de Deux Mots, Theoretical Computer Science, 1986], we show in this paper that it is NP-complete to determine whether or not a word u is a square for the shuffle product. The novelty in our approach lies in representing words as linear graphs, in which deciding whether or not a given word is a square for the shuffle product reduces to computing some inclusion-free perfect matching.

Keywords

Perfect Match Linear Graph Input Word Identical Letter Discrete Apply Mathematic 
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 2013

Authors and Affiliations

  • Romeo Rizzi
    • 1
  • Stéphane Vialette
    • 2
  1. 1.Dipartimento di Matematica ed InformaticaUniversità degli Studi di UdineItaly
  2. 2.LIGM CNRS UMR 8049Université Paris-EstFrance

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