Consensus string problem for multiple regular languages

Yo Sub Han; Sang Ki Ko; Timothy Ng; Kai Salomaa

doi:10.1016/j.ic.2020.104615

Consensus string problem for multiple regular languages

Yo Sub Han, Sang Ki Ko, Timothy Ng, Kai Salomaa

College of Computing

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The consensus string (or centre string, closest string) of a set S of strings is defined as a string which is within a radius r from all strings in S. We study the consensus string problem for multiple languages recognized by finite automata (FAs). We define the consensus string of languages to be within distance at most r to some string in each of the languages. We also study the decidability and computational complexity of the consensus string problem for multiple formal language instances. We show that the consensus string problem for multiple regular languages is PSPACE-complete even when the radius r is fixed. We prove that the problem can be solved in polynomial time when the number of languages is fixed. Finally, we study that the consensus string problem for the class of input-driven languages and show that the problem is decidable.

Original language	English
Article number	104615
Journal	Information and Computation
Volume	279
DOIs	https://doi.org/10.1016/j.ic.2020.104615
Publication status	Published - 2021 Aug

Bibliographical note

Funding Information:
Han was supported by the Institute for Information & communications Technology Promotion (IITP) grant funded by the Korea government (MSIP) ( 2018-0-00276 ) and Salomaa was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) ( OGP0147224 ).

Publisher Copyright:
© 2020 Elsevier Inc.

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Computer Science Applications
Computational Theory and Mathematics

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10.1016/j.ic.2020.104615

Cite this

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title = "Consensus string problem for multiple regular languages",

abstract = "The consensus string (or centre string, closest string) of a set S of strings is defined as a string which is within a radius r from all strings in S. We study the consensus string problem for multiple languages recognized by finite automata (FAs). We define the consensus string of languages to be within distance at most r to some string in each of the languages. We also study the decidability and computational complexity of the consensus string problem for multiple formal language instances. We show that the consensus string problem for multiple regular languages is PSPACE-complete even when the radius r is fixed. We prove that the problem can be solved in polynomial time when the number of languages is fixed. Finally, we study that the consensus string problem for the class of input-driven languages and show that the problem is decidable.",

author = "Han, {Yo Sub} and Ko, {Sang Ki} and Timothy Ng and Kai Salomaa",

note = "Funding Information: Han was supported by the Institute for Information & communications Technology Promotion (IITP) grant funded by the Korea government (MSIP) ( 2018-0-00276 ) and Salomaa was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) ( OGP0147224 ). Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

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AU - Salomaa, Kai

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PY - 2021/8

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N2 - The consensus string (or centre string, closest string) of a set S of strings is defined as a string which is within a radius r from all strings in S. We study the consensus string problem for multiple languages recognized by finite automata (FAs). We define the consensus string of languages to be within distance at most r to some string in each of the languages. We also study the decidability and computational complexity of the consensus string problem for multiple formal language instances. We show that the consensus string problem for multiple regular languages is PSPACE-complete even when the radius r is fixed. We prove that the problem can be solved in polynomial time when the number of languages is fixed. Finally, we study that the consensus string problem for the class of input-driven languages and show that the problem is decidable.

AB - The consensus string (or centre string, closest string) of a set S of strings is defined as a string which is within a radius r from all strings in S. We study the consensus string problem for multiple languages recognized by finite automata (FAs). We define the consensus string of languages to be within distance at most r to some string in each of the languages. We also study the decidability and computational complexity of the consensus string problem for multiple formal language instances. We show that the consensus string problem for multiple regular languages is PSPACE-complete even when the radius r is fixed. We prove that the problem can be solved in polynomial time when the number of languages is fixed. Finally, we study that the consensus string problem for the class of input-driven languages and show that the problem is decidable.

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Consensus string problem for multiple regular languages

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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