no. 1
An aperiodicity problem for multiwords
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 1, pp. 33-50.

Multiwords are words in which a single symbol can be replaced by a nonempty set of symbols. They extend the notion of partial words. A word w is certain in a multiword M if it occurs in every word that can be obtained by selecting one single symbol among the symbols provided in each position of M. Motivated by a problem on incomplete databases, we investigate a variant of the pattern matching problem which is to decide whether a word w is certain in a multiword M. We study the language CERTAIN(w) of multiwords in which w is certain. We show that this regular language is aperiodic for three large families of words. We also show its aperiodicity in the case of partial words over an alphabet with at least three symbols.

DOI : 10.1051/ita/2011131
Classification : 68R15, 68Q45
Mots clés : pattern matching, aperiodicity, partial words 
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     author = {Bruy\`ere, V\'eronique and Carton, Olivier and Decan, Alexandre and Gauwin, Olivier and Wijsen, Jef},
     title = {An aperiodicity problem for multiwords},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {33--50},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {1},
     year = {2012},
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     mrnumber = {2904959},
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     url = {http://www.numdam.org/articles/10.1051/ita/2011131/}
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Bruyère, Véronique; Carton, Olivier; Decan, Alexandre; Gauwin, Olivier; Wijsen, Jef. An aperiodicity problem for multiwords. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 1, pp. 33-50. doi : 10.1051/ita/2011131. http://www.numdam.org/articles/10.1051/ita/2011131/

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