@inproceedings{483fa949989a4b1b9623ad73cc08138b,

title = "A partially synchronizing coloring",

abstract = "Given a finite directed graph, a coloring of its edges turns the graph into a finite-state automaton. A k-synchronizing word of a deterministic automaton is a word in the alphabet of colors at its edges that maps the state set of the automaton at least on k-element subset. A coloring of edges of a directed strongly connected finite graph of a uniform outdegree (constant outdegree of any vertex) is k-synchronizing if the coloring turns the graph into a deterministic finite automaton possessing a k-synchronizing word. For k = 1 one has the well known road coloring problem. The recent positive solution of the road coloring problem implies an elegant generalization considered first by B{\'e}al and Perrin: a directed finite strongly connected graph of uniform outdegree is k-synchronizing iff the greatest common divisor of lengths of all its cycles is k. Some consequences for coloring of an arbitrary finite digraph are presented. We describe a subquadratic algorithm of the road coloring for the k-synchronization implemented in the package TESTAS. A new linear visualization program demonstrates the obtained coloring. Some consequences for coloring of an arbitrary finite digraph and of such a graph of uniform outdegree are presented.",

keywords = "algorithm, deterministic finite automaton, graph, road coloring, synchronization",

author = "Trahtman, {Avraham N.}",

year = "2010",

doi = "10.1007/978-3-642-13182-0_36",

language = "אנגלית",

isbn = "3642131816",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "362--370",

booktitle = "Computer Science - Theory and Applications - 5th International Computer Science Symposium in Russia, CSR 2010, Proceedings",

note = "5th International Computer Science Symposium in Russia, CSR 2010 ; Conference date: 16-06-2010 Through 20-06-2010",

}