On recognising words that are squares for the shuffle product - ESIEE Paris Access content directly
Journal Articles Theoretical Computer Science Year : 2023

On recognising words that are squares for the shuffle product

Abstract

The shuffle of two words u and v of A is the language uv consisting of all words u1v1u2v2ukvk, where k0 and the ui and vi are words of A such that u=u1u2uk and v=v1v2vk. In other words, uv is the finite set of all words obtainable from merging the words u and v from left to right, but choosing the next symbol arbitrarily from u or v. A word uA is a square for the shuffle product if it is the shuffle of two identical words (i.e., uvv for some vA).

Whereas it can be decided in polynomial-time whether or not uv1v2 for given words u, v1 and v2 (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.

Fichier principal
Vignette du fichier
RizziVialetteTCS2023.pdf (413.44 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04498180 , version 1 (11-03-2024)

Identifiers

Cite

Romeo Rizzi, Stéphane Vialette. On recognising words that are squares for the shuffle product. Theoretical Computer Science, 2023, 956, pp.111156.1-16. ⟨10.1016/j.tcs.2017.04.003⟩. ⟨hal-04498180⟩
134 View
14 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More