@inproceedings{c4ed869827404966b7e74d250045980e,
title = "Closest Substring Problems for Regular Languages",
abstract = "It is well known that given a finite set of strings of equal length, the Consensus String problem—the problem of deciding whether or not there exists a consensus string whose distance is at most r from every string in the given set—is proven to be NP-complete. A similar problem called the Closest Substring problem asks whether there exists a string w of length l such that each string in a given set L has a substring whose distance is at most r (called radius) from w. As the Closest Substring problem is a generalized version of the Consensus String problem, it is obvious that the problem is NP-hard for a finite set of strings. We show that the Closest Substring problem for regular languages represented by nondeterministic finite automata (NFAs) is PSPACE-complete. The main difference from the previous work is that we consider an infinite set of strings, which is recognized by an NFA as input instead of a finite set of strings. We also prove that the Closest Substring problem for acyclic NFAs lies in the second level of the polynomial-time hierarchy (formula presented) and is both NP-hard and coNP-hard.",
author = "Han, {Yo Sub} and Ko, {Sang Ki} and Timothy Ng and Kai Salomaa",
year = "2018",
month = jan,
day = "1",
doi = "10.1007/978-3-319-98654-8_32",
language = "English",
isbn = "9783319986531",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "392--403",
editor = "Mizuho Hoshi and Shinnosuke Seki",
booktitle = "Developments in Language Theory - 22nd International Conference, DLT 2018, Proceedings",
address = "Germany",
note = "22nd International Conference on Developments in Language Theory, DLT 2018 ; Conference date: 10-09-2018 Through 14-09-2018",
}