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arXiv · 1404.3311

Generating Synchronizing Automata with Large Reset Lengths

Andrzej Kisielewicz·Marek Szykuła
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Abstract

We study synchronizing automata with the shortest reset words of relatively large length. First, we refine the Frankl-Pin result on the length of the shortest words of rank $m$, and the B\'eal, Berlinkov, Perrin, and Steinberg results on the length of the shortest reset words in one-cluster automata. The obtained results are useful in computation aimed in extending the class of small automata for which the \v{C}ern\'y conjecture is verified and discovering new automata with special properties regarding synchronization.

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Andrzej Kisielewicz, Marek Szykuła. 2014-04-12. Generating Synchronizing Automata with Large Reset Lengths. https://arxiv.org/abs/1404.3311

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