Disjoint pattern matching and implication in strings

13 years 3 months ago

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We deal with the problem of deciding whether a given set of string patterns implies the presence of a ﬁxed pattern. While checking whether a set of patterns occurs in a string is solvable in polynomial time, this implication problem is well-known to be intractable. Here we consider a version of the problem when patterns in the set are required to be disjoint. We show that for such a version of the problem the situation is reversed: checking whether a set of patterns occurs in a string is NP-complete, but the implication problem is solvable in polynomial time.

Leonid Libkin, Cristina Sirangelo

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