| import OAI.Combinatorics.LowSpaceSubsetSum.Word.WordRangeRealization |
| import OAI.Combinatorics.LowSpaceSubsetSum.Counting.PrimeSamplerCoupling |
| import OAI.Combinatorics.LowSpaceSubsetSum.Compression.CompressionSamplerCoupling |
|
|
| namespace OAI |
|
|
| /-! # Word refinements for the prime calls used in both branches -/ |
|
|
| noncomputable section |
| namespace LowSpaceSubsetSum.WordRealization |
|
|
| def prime (w n ell : ℕ) (hell : 4 ≤ ell) (hw : ell ≤ w) : |
| Realization w (n^3) (primeCoupling hell n) := by |
| let : Nonempty ↥(primeRange ell) := (primeRange_nonempty hell).to_subtype |
| let : Nonempty {x : Fin (2 ^ ell) // primeEligible ell x} := |
| ⟨(primeEligibleEquiv hell).symm (Classical.choice inferInstance)⟩ |
| exact map (rejection w ell hw (n^3) (primeEligible ell)) (primeEligibleEquiv hell) |
|
|
| def factor (w n ell : ℕ) (hw : ell ≤ w) : |
| Realization w (n^3) (factorCoupling n ell) := by |
| unfold factorCoupling |
| split |
| next h => exact enlarge (map (pure ()) (factorOneEquiv h)) (Nat.zero_le _) |
| next h => exact map (prime w n ell (by omega) hw) (factorPrimeEquiv (by omega)) |
|
|
| def triplePrime (w n a b c : ℕ) (ha : a ≤ w) (hb : b ≤ w) (hc : c ≤ w) : |
| Realization w (3*n^3) (triplePrimeCoupling n a b c) := by |
| have h := map (prod (prod (factor w n a ha) (factor w n b hb)) |
| (factor w n c hc)) (tripleFactorEquiv a b c) |
| simpa only [triplePrimeCoupling, show (n^3+n^3)+n^3 = 3*n^3 by omega] using h |
|
|
| def compression {n : ℕ} (D : CompressionData n) (hn : 168000000 ≤ n) |
| (w : ℕ) (hp : Nat.clog 2 n ≤ w) (hq : compressionPrimeExponent n ≤ w) : |
| Realization w (n*n^3+n^3) (D.sampler hn) := |
| bind (permutation w n n hp) (fun _ => CompressionSetup.PrimeSpace n) |
| (fun _ => primeCoupling (by unfold compressionPrimeExponent; omega) n) |
| (fun _ => prime w n (compressionPrimeExponent n) |
| (by unfold compressionPrimeExponent; omega) hq) |
|
|
| end LowSpaceSubsetSum.WordRealization |
|
|
| end |
|
|
| end OAI |
|
|
