Source labels openChecked July 26, 2026

Černý Conjecture

Černý Conjecture*: Every synchronizing DFA with $n$ states admits a synchronizing word of length at most $(n - 1)^2$ .

Computer science AMS 68

Mathematical statement

Černý Conjecture*: Every synchronizing DFA with $n$ states admits a synchronizing word of length at most $(n - 1)^2$ .

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

cerny_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem cerny_conjecture :    answer(sorry) ↔ ∀ {α : Type*} {σ : Type*} [Fintype σ] (M : DFA α σ) (hM : M.IsSynchronizing) ,    ∃ w : List α, M.IsSynchronizingWord w ∧ w.length ≤ (Fintype.card σ - 1)^2 := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization Wikipedia: Synchronizing wordbackground *Poznámka k homogénnym experimentom s konečnými automatmi*background