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arXiv · 2407.08135

A quadratic upper bound on the reset thresholds of synchronizing automata containing a transitive permutation group

Yinfeng Zhu
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Abstract

For any synchronizing $n$-state deterministic automaton, Černý conjectures the existence of a synchronizing word of length at most $(n-1)^2$. We prove that there exists a synchronizing word of length at most $2n^2 - 7n + 7$ for every synchronizing $n$-state deterministic automaton that satisfies the following two properties: 1. The image of the action of each letter contains at least $n-1$ states; 2. The actions of bijective letters generate a transitive permutation group on the state set.

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Yinfeng Zhu. 2024-07-11. A quadratic upper bound on the reset thresholds of synchronizing automata containing a transitive permutation group. https://arxiv.org/abs/2407.08135

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