TY - GEN

T1 - The road coloring and Černy conjecture

AU - Trahtman, Avraham N.

PY - 2008

Y1 - 2008

N2 - A synchronizing word of a deterministic automaton is a word in the alphabet of colors (considered as letters) of its edges that maps the automaton to a single state. A coloring of edges of a directed graph is synchronizing if the coloring turns the graph into a deterministic finite automaton possessing a synchronizing word. The road coloring problem is the problem of synchronizing coloring of a directed finite strongly connected graph with constant outdegree of all its vertices if the greatest common divisor of lengths of all its cycles is one. The problem was posed by Adler, Goodwyn and Weiss over 30 years ago and evoked noticeable interest among the specialists in the theory of graphs, deterministic automata and symbolic dynamics. The positive solution of the road coloring problem is presented. Some consequences on the length of the synchronizing word are discussed.

AB - A synchronizing word of a deterministic automaton is a word in the alphabet of colors (considered as letters) of its edges that maps the automaton to a single state. A coloring of edges of a directed graph is synchronizing if the coloring turns the graph into a deterministic finite automaton possessing a synchronizing word. The road coloring problem is the problem of synchronizing coloring of a directed finite strongly connected graph with constant outdegree of all its vertices if the greatest common divisor of lengths of all its cycles is one. The problem was posed by Adler, Goodwyn and Weiss over 30 years ago and evoked noticeable interest among the specialists in the theory of graphs, deterministic automata and symbolic dynamics. The positive solution of the road coloring problem is presented. Some consequences on the length of the synchronizing word are discussed.

KW - Deterministic finite automaton

KW - Graph

KW - Road coloring problem

KW - Synchronization

UR - http://www.scopus.com/inward/record.url?scp=77954597166&partnerID=8YFLogxK

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AN - SCOPUS:77954597166

SN - 9788001041451

T3 - Proceedings of the Prague Stringology Conference 2008

SP - 1

EP - 12

BT - Proceedings of the Prague Stringology Conference 2008

T2 - Prague Stringology Conference 2008, PSC 2008

Y2 - 1 September 2008 through 3 September 2008

ER -