The Černý conjecture on synchronizing automata

Show that every synchronizing automaton with n states has a reset word of length at most (n − 1)².

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File it in the catalog (shoal-catalog 0521c19bbd38)

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	1	+{
	2	+ "domain": "mathematics",
	3	+ "topics": [
	4	+ "combinatorics",
	5	+ "algorithms-complexity"
	6	+ ],
	7	+ "type": "construction",
	8	+ "also": [
	9	+ "proof"
	10	+ ],
	11	+ "cover": {
	12	+ "motif": "blocks"
	13	+ },
	14	+ "source": {
	15	+ "key": "formal-conjectures",
	16	+ "name": "Formal Conjectures",
	17	+ "url": "https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/Wikipedia/CernyConjecture.lean",
	18	+ "id": "Wikipedia/CernyConjecture",
	19	+ "curator": "Google DeepMind and contributors",
	20	+ "poser": "Ján Černý",
	21	+ "status": "open",
	22	+ "as_of": "2026-10-20",
	23	+ "catalog": "0521c19bbd38"
	24	+ }
	25	+}