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An aperiodicity problem for multiwords

Published online by Cambridge University Press:  23 November 2011

Véronique Bruyère
Affiliation:
Universitéde Mons – UMONS, Institut d’Informatique, Belgium. first.last@umons.ac.be
Olivier Carton
Affiliation:
Université Paris Diderot, LIAFA, France; olivier.carton@liafa.jussieu.fr
Alexandre Decan
Affiliation:
Universitéde Mons – UMONS, Institut d’Informatique, Belgium. first.last@umons.ac.be
Olivier Gauwin
Affiliation:
Universitéde Mons – UMONS, Institut d’Informatique, Belgium. first.last@umons.ac.be
Jef Wijsen
Affiliation:
Universitéde Mons – UMONS, Institut d’Informatique, Belgium. first.last@umons.ac.be
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Abstract

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.

Type
Research Article
Copyright
© EDP Sciences 2011

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