The \v{C}ern\'{y} conjecture for small automata: experimental report
Jakub Kowalski, Marek Szyku{\l}a

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.
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Taxonomy
Topicssemigroups and automata theory · DNA and Biological Computing · Machine Learning and Algorithms
