Some new Features and Algorithms for the Study of DFA

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.