The Visualization of the Road Coloring Algorithm in the package TESTAS

TL;DR

This paper discusses a visualization tool for the road coloring algorithm, which is used to find synchronizing colorings of directed graphs, aiding understanding of the automaton's structure.

Contribution

It introduces a new visualization program for the road coloring algorithm and automata transition graphs, enhancing comprehension and analysis.

Findings

Visualization helps demonstrate the algorithm's process.

The tool is efficient, with linear complexity.

It reveals structural properties of automata transition graphs.

Abstract

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 with constant outdegree of all its vertices if the greatest common divisor of the lengths of all its cycles is one. A polynomial time algorithm of the road coloring has been based on recent positive solution of this old famous problem. One can use our new visualization program for demonstration of the algorithm as well as for visualization of the transition graph of any finite automaton. The visual image presents some structure properties of the transition graph. This help tool is linear in the size of the automaton.