On recognising words that are squares for the shuffle product
Abstract
Whereas it can be decided in polynomial-time whether or not for given words u, and (J.-C. Spehner, 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. Finally, we prove that it is NP-complete to determine whether or not an input word is in the shuffle of a word with its reverse.
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