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Complexity of road coloring with prescribed reset words.

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Bibliographic Details
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]
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Database: Engineering Source
Description
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]
ISSN:00220000
DOI:10.1016/j.jcss.2016.05.009