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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.
| 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 | "review": true, |
| 26 | "approval": "first-time" |
| 27 | } |