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This is a Literature Review study.

October 3, 2025Open Access

List of Results on the Černý Conjecture and Reset Thresholds for Synchronizing Automata

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The Černý conjecture has been proven for several classes of finite automata, indicating progress in this area of study.
A quadratic upper bound on the minimum length of reset words is established for some classes, which shows partial resolution.
The survey presents a snapshot of findings in synchronizing automata as of September 5, 2025, reflecting ongoing research efforts.
Classes of finite automata for which the Černý conjecture is still unresolved are also identified, pointing to future research directions.

Implication

This survey details the Černý conjecture outcomes in finite automata, highlighting known constraints and open classes.

Abstract

We survey results in the literature that establish the Černý conjecture for various classes of finite automata. We also list classes for which the conjecture remains open, but a quadratic (in the number of states) upper bound on the minimum length of reset words is known. The results presented reflect the state of the art as of September 5, 2025.

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Cite This Study

Mikhail V. Volkov (2025) studied this question.

synapsesocial.com/papers/68e02f40f0e39f13e7fa28c0 https://doi.org/10.48550/arxiv.2508.15655

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Implication

This survey details the Černý conjecture outcomes in finite automata, highlighting known constraints and open classes.

List of Results on the Černý Conjecture and Reset Thresholds for Synchronizing Automata

Key Points

Implication

Abstract

Discussion

Cite This Study

List of Results on the Černý Conjecture and Reset Thresholds for Synchronizing Automata

Key Points

Implication

Abstract

Discussion

Cite This Study

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