The Visualization of the Road Coloring Algorithm in the package TESTAS

A problem of a visual image of a directed finite graph has appeared in the study of the road coloring conjecture. Given a finite directed graph, a coloring of its edges turns the graph into finite-state automaton. The visual perception of the structure properties of automata is an important goal. A synchronizing word of a deterministic automaton is a word in the alphabet of colors 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. A polynomial time algorithm of the road coloring has been based on recent positive solution of this old famous problem. Our visualization program is used for demonstration of the algorithm as well as for visualization of the transition graph of any deterministic finite automaton (DFA). This help tool is linear in the size of the automaton.