Some new Features and Algorithms for the Study of DFA

TL;DR

This paper introduces new algorithms implemented in TESTAS for analyzing DFA synchronization, including methods for finding short and minimal synchronizing words, and algorithms for road coloring and graph visualization.

Contribution

It presents novel algorithms for DFA synchronization analysis, including procedures for finding short and minimal synchronizing words and for road coloring based on graph properties.

Findings

Algorithms successfully identify synchronizing words of minimal length.

Effective procedures for road coloring of directed graphs.

Linear visualization enhances understanding of automaton structure.

Abstract

The work presents some new algorithms realized recently in the package TESTAS. They decide whether or not deterministic finite automaton (DFA) is synchronizing, several procedures find relatively short synchronizing words and a synchronizing word of the minimal length. We check the existence of a coloring of directed graph that turns the graph into a synchronizing DFA. The algorithm finds the coloring (better known as the road coloring) if it exists. Otherwise, the k-synchronizing road coloring can be found. We use a linear visualization of the graph of an automaton based on its structural properties.