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Complexity of road coloring with prescribed reset words.

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Title: Complexity of road coloring with prescribed reset words.
Authors: Vorel, Vojtěch1 (AUTHOR) vorel@ktiml.mff.cuni.cz, Roman, Adam1,2 (AUTHOR) roman@ii.uj.edu.pl
Source: Journal of Computer & System Sciences. Sep2019, Vol. 104, p342-358. 17p.
Subjects: Coloring matter, Polynomial time algorithms, Statistical decision making, Multigraph, Vocabulary
Abstract: By the Road Coloring Theorem (Trahtman, 2008), the edges of any given aperiodic strongly connected directed multigraph with a constant out-degree can be colored such that the resulting automaton admits a reset word. There may also be a need for a particular reset word to be admitted. In this paper we consider the following problem: given a word w and digraph G , is it true that G has a coloring that is synchronized by w ? We show that it is NP-complete for certain fixed words. For the binary alphabet we present a classification that separates such words from those that make the problem solvable in polynomial time. The classification differs if we consider only strongly connected multigraphs. In this restricted setting the classification remains incomplete. • We consider complexity of synchronization-related decision problem. • We parameterize the problem by set of words, alphabet size and graph classes. • We find the complexity classes for one word sets. • The complexity depends on the family of the considered graph types. • The complexity depends on the word, when alphabet and graph classes are fixed. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Computer & System Sciences is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Complexity of road coloring with prescribed reset words.
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  Data: <searchLink fieldCode="AR" term="%22Vorel%2C+Vojtěch%22">Vorel, Vojtěch</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> vorel@ktiml.mff.cuni.cz</i><br /><searchLink fieldCode="AR" term="%22Roman%2C+Adam%22">Roman, Adam</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> roman@ii.uj.edu.pl</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Computer+%26+System+Sciences%22">Journal of Computer & System Sciences</searchLink>. Sep2019, Vol. 104, p342-358. 17p.
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  Data: <searchLink fieldCode="DE" term="%22Coloring+matter%22">Coloring matter</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomial+time+algorithms%22">Polynomial time algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+decision+making%22">Statistical decision making</searchLink><br /><searchLink fieldCode="DE" term="%22Multigraph%22">Multigraph</searchLink><br /><searchLink fieldCode="DE" term="%22Vocabulary%22">Vocabulary</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: By the Road Coloring Theorem (Trahtman, 2008), the edges of any given aperiodic strongly connected directed multigraph with a constant out-degree can be colored such that the resulting automaton admits a reset word. There may also be a need for a particular reset word to be admitted. In this paper we consider the following problem: given a word w and digraph G , is it true that G has a coloring that is synchronized by w ? We show that it is NP-complete for certain fixed words. For the binary alphabet we present a classification that separates such words from those that make the problem solvable in polynomial time. The classification differs if we consider only strongly connected multigraphs. In this restricted setting the classification remains incomplete. • We consider complexity of synchronization-related decision problem. • We parameterize the problem by set of words, alphabet size and graph classes. • We find the complexity classes for one word sets. • The complexity depends on the family of the considered graph types. • The complexity depends on the word, when alphabet and graph classes are fixed. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Computer & System Sciences is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.jcss.2016.05.009
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 17
        StartPage: 342
    Subjects:
      – SubjectFull: Coloring matter
        Type: general
      – SubjectFull: Polynomial time algorithms
        Type: general
      – SubjectFull: Statistical decision making
        Type: general
      – SubjectFull: Multigraph
        Type: general
      – SubjectFull: Vocabulary
        Type: general
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      – TitleFull: Complexity of road coloring with prescribed reset words.
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            NameFull: Vorel, Vojtěch
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            NameFull: Roman, Adam
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            – D: 01
              M: 09
              Text: Sep2019
              Type: published
              Y: 2019
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              Value: 104
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