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On Recognizing Words That Are Squares for the Shuffle Product

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Part of the Lecture Notes in Computer Science book series (LNTCS,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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Rizzi, R., Vialette, S. (2013). On Recognizing Words That Are Squares for the Shuffle Product. In: Bulatov, A.A., Shur, A.M. (eds) Computer Science – Theory and Applications. CSR 2013. Lecture Notes in Computer Science, vol 7913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38536-0_21

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  • DOI: https://doi.org/10.1007/978-3-642-38536-0_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38535-3

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