A Variant of Pattern Matching for Multiwords

Multiwords are words in which a single symbol can be replaced by a nonempty set of symbols. A pattern 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 pattern 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 and we study the size of its minimal automaton.

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