# An aperiodicity problem for multiwords

Véronique Bruyère; Olivier Carton; Alexandre Decan; Olivier Gauwin; Jef Wijsen

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2012)

- Volume: 46, Issue: 1, page 33-50
- ISSN: 0988-3754

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topBruyère, Véronique, et al. "An aperiodicity problem for multiwords." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 46.1 (2012): 33-50. <http://eudml.org/doc/272983>.

@article{Bruyère2012,

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.},

author = {Bruyère, Véronique, Carton, Olivier, Decan, Alexandre, Gauwin, Olivier, Wijsen, Jef},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {pattern matching; aperiodicity; partial words},

language = {eng},

number = {1},

pages = {33-50},

publisher = {EDP-Sciences},

title = {An aperiodicity problem for multiwords},

url = {http://eudml.org/doc/272983},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Bruyère, Véronique

AU - Carton, Olivier

AU - Decan, Alexandre

AU - Gauwin, Olivier

AU - Wijsen, Jef

TI - An aperiodicity problem for multiwords

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2012

PB - EDP-Sciences

VL - 46

IS - 1

SP - 33

EP - 50

AB - 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.

LA - eng

KW - pattern matching; aperiodicity; partial words

UR - http://eudml.org/doc/272983

ER -

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