File size: 871 Bytes
ea76aac | 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 26 | import OAI.Computability.LoopMatching.LiteralChoices
import OAI.Computability.LoopMatching.SmallBoundary
import OAI.Computability.LoopMatching.Main
namespace OAI
namespace LoopMatchingReference
theorem challenge :
∃ A : LoopMatching.Input → ℕ × ℕ,
∃ machine : Turing.TM2ComputableInPolyTime
LoopMatching.encodeInput LoopMatching.encodeOutput A,
(∀ k, Finite (machine.tm.Γ k)) ∧
(∃ P : Polynomial ℕ, ∀ G,
(LoopMatching.encodeOutput (A G)).length ≤
P.eval (LoopMatching.encodeInput G).length) ∧
∀ G, 0 < (A G).2 ∧
(A G).1 ≤ (A G).2 * LoopMatching.count G ∧
(A G).2 * LoopMatching.count G ≤ 2 ^ (18 * G.n) * (A G).1 ∧
((A G).1 = 0 ↔ LoopMatching.count G = 0) := by
exact LoopMatching.fullEndpoint
end LoopMatchingReference
end OAI
|