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arXiv · 2608.24245

Synchronizing Automata: Open Problems

Marek Szykuła
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Abstract

We survey selected open problems in the theory of synchronizing automata, centered around the famous Černý conjecture. A deterministic finite automaton is called synchronizing if it admits a reset word whose action maps all states to a single state. The Černý conjecture states that every synchronizing automaton with n states possesses a reset word of length at most (n-1)^2. We discuss avoiding words, compressing a state with another, synchronization of a (given or any) subset, complexity of deciding the synchronizability, average reset threshold, and linear-algebraic methods. Some new auxiliary results are also presented.

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Marek Szykuła. 2026-08-25. Synchronizing Automata: Open Problems. https://doi.org/10.4204/eptcs.451.3

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