A. N. Trahtman. The Road Coloring Problem


Natural Sciences / Computer Science / Automata theory

Submitted on: Apr 01, 2012, 20:57:48

Description: 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 alits 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.

The abstract of this article has been published in the "Intellectual Archive Bulletin" , April 2012, ISSN 1929-1329.

The Library of Congress (USA) reference page : http://lccn.loc.gov/2012210064.
The Library and Archives Canada reference page: collectionscanada.gc.ca/ourl/res.php?url_ver=Z39.88......

To read the article posted on Intellectual Archive web site please click the link below.

A_N_Trahtman_road_coloring_problem.pdf



© 2011-2017 Shiny World Corp. All rights reserved. To reach us please send an e-mail to support@IntellectualArchive.com