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.
| Original language | English |
|---|---|
| Title of host publication | Developments in Language Theory - 22nd International Conference, DLT 2018, Proceedings |
| Editors | Mizuho Hoshi, Shinnosuke Seki |
| Publisher | Springer Verlag |
| Pages | 392-403 |
| Number of pages | 12 |
| ISBN (Print) | 9783319986531 |
| DOIs | |
| Publication status | Published - 2018 Jan 1 |
| Event | 22nd International Conference on Developments in Language Theory, DLT 2018 - Tokyo, Japan Duration: 2018 Sep 10 → 2018 Sep 14 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 11088 LNCS |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
Other
| Other | 22nd International Conference on Developments in Language Theory, DLT 2018 |
|---|---|
| Country | Japan |
| City | Tokyo |
| Period | 18/9/10 → 18/9/14 |
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)
Cite this
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Closest Substring Problems for Regular Languages. / Han, Yo Sub; Ko, Sang Ki; Ng, Timothy; Salomaa, Kai.
Developments in Language Theory - 22nd International Conference, DLT 2018, Proceedings. ed. / Mizuho Hoshi; Shinnosuke Seki. Springer Verlag, 2018. p. 392-403 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11088 LNCS).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
TY - GEN
T1 - Closest Substring Problems for Regular Languages
AU - Han, Yo Sub
AU - Ko, Sang Ki
AU - Ng, Timothy
AU - Salomaa, Kai
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=85053888367&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-98654-8_32
DO - 10.1007/978-3-319-98654-8_32
M3 - Conference contribution
SN - 9783319986531
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 392
EP - 403
BT - Developments in Language Theory - 22nd International Conference, DLT 2018, Proceedings
A2 - Hoshi, Mizuho
A2 - Seki, Shinnosuke
PB - Springer Verlag
ER -