The road coloring problem

Details The road coloring problem The road coloring problem

2007-09-02

arxiv.org/abs/0709.0099v4

Computer Science

Discrete Mathematics

9 pages, correct typos

Scientific paper

The synchronizing word of 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 deterministic finite automaton possessing a synchronizing word. The road coloring problem is a problem of synchronizing coloring of 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 a noticeable interest among the specialists in theory of graphs, deterministic automata and symbolic dynamics. The problem is described even in "Wikipedia" - the popular Internet Encyclopedia. The positive solution of the road coloring problem is presented.

Affiliated with

Also associated with

No associations

Rating

The road coloring problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The road coloring problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The road coloring problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-688728