Disjoint pattern matching and implication in strings

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.

• Type: Journal
• Year: 2010
• Where: IPL
• Authors: Leonid Libkin, Cristina Sirangelo
• Keywords: Implication Problem, IPL 2010, Polynomial Time, String