Closest substring problems for regular languages

초록

The CLOSEST SUBSTRING problem asks whether there exists a consensus string w of given length l such that each string in a set of strings L has a substring whose edit distance is at most r (called the radius) from w. The CLOSEST SUBSTRING problem has been studied for finite sets of strings and is known to be NP-hard. We show that the CLOSEST SUBSTRING problem for regular languages represented by nondeterministic finite automata (NFA) is PSPACE-complete. The problem remains PSPACE-hard even when the input is a deterministic finite automaton and the length l and radius r are given in unary. Also we show that the CLOSEST SUBSTRING problem for acyclic NFAs lies in the second level of the polynomial-time hierarchy and is both NP-hard and coNP-hard. (C) 2020 Elsevier B.V. All rights reserved.

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