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

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 January 13, 2026.

29 pages, 5 figures. In the version of January 13, 2025, the bibliography has been updated