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c270adf | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | import Mathlib
import OAI.Combinatorics.IndependentSets.Model
namespace OAI
namespace LargeIndependentSets
structure GraphReduction (δ : ℚ) where
reduce : List Bool → Graph
computation : Turing.TM2ComputableInPolyTime (id : List Bool → List Bool) graphBits reduce
finiteAlphabets : ∀ k : computation.tm.K, Finite (computation.tm.Γ k)
outputBound : Polynomial ℕ
outputSize : ∀ b, (graphBits (reduce b)).length ≤ outputBound.eval b.length
completeness : ∀ φ : Formula, φ.Satisfiable → (reduce (formulaBits φ)).ThreeColorable
soundness : ∀ φ : Formula, ¬φ.Satisfiable →
((reduce (formulaBits φ)).independenceNumber : ℚ) <
δ * (reduce (formulaBits φ)).vertices
def MainStatement : Prop :=
∀ δ : ℚ, 0 < δ → δ < 1 / 3 → Nonempty (GraphReduction δ)
end LargeIndependentSets
end OAI
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