Implementation of the algorithm for testing an automaton for synchronization in linear expected time

TL;DR

This paper presents an implementation and experimental evaluation of a linear expected time algorithm for testing automaton synchronization, improving over traditional quadratic methods and providing statistical insights into automaton properties.

Contribution

The authors modify and implement Berlinkov's linear-time algorithm, demonstrating its efficiency and enabling statistical analysis of automaton synchronization properties.

Findings

Implementation outperforms quadratic algorithms on modest automata sizes.

Experimental results confirm the linear expected time performance.

Provides statistical estimates of non-synchronizing automata ratio.

Abstract

Berlinkov has suggested an algorithm that, given a deterministic finite automaton $\mathcal{A}$, verifies whether or not $\mathcal{A}$ is synchronizing in linear (of the number of states and letters) expected time. We present a modification of Berlinkov's algorithm which we have implemented and tested. Our experiments show that the implementation outperforms the standard quadratic algorithm even for automata of modest size and allow us to give a statistically accurate approximation of the ratio of non-synchronizing automata amongst all automata with a given number of states.