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structure definition def or abbrev

RSATSeparation

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formal statement (Lean)

 247structure RSATSeparation where
 248  /-- SAT is solvable in O(n) recognition steps for satisfiable instances -/
 249  sat_polytime : ∀ n : ℕ, ∀ f : CNFFormula n, f.isSAT →
 250    ∃ steps : ℕ, steps ≤ n ∧ ∃ a : Assignment n, satJCost f a = 0
 251  /-- No local certifier works for all formulas (adversarial failure) -/
 252  local_certifier_fails : ∀ n : ℕ, ∀ M : Finset (Fin n),
 253    M.card < n →
 254    ∃ b : Bool, ∃ R : Fin n → Bool,
 255      ∃ g : ({i // i ∈ M} → Bool) → Bool,
 256        g (BalancedParityHidden.restrict (BalancedParityHidden.enc b R) M) ≠ b
 257  /-- UNSAT instances have a persistent topological obstruction -/
 258  unsat_obstruction : ∀ n : ℕ, ∀ f : CNFFormula n, f.isUNSAT →
 259    ∀ a : Assignment n, satJCost f a ≥ 1
 260

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