The \v{C}ern\'{y} conjecture for small automata: experimental report

TL;DR

This paper reports experimental verification of the Černý conjecture for small automata with up to 11 states, revealing new insights into reset words and automata classes.

Contribution

It provides the first comprehensive computational verification of the Černý conjecture for automata with up to 11 states and uncovers new phenomena in automata synchronization.

Findings

Confirmed the conjecture for automata with up to 11 states

Discovered the third gap in shortest reset word distribution

Identified new slowly synchronizing automata classes

Abstract

We present a report from a series of experiments involving computation of the shortest reset words for automata with small number of states. We confirm that the \v{C}ern\'{y} conjecture is true for all automata with at most 11 states on 2 letters. Also some new interesting results were obtained, including the third gap in the distribution of the shortest reset words and new slowly synchronizing classes of automata.