| import OAI.Combinatorics.LowSpaceSubsetSum.Storage.SamplerPiCells |
| import OAI.Combinatorics.LowSpaceSubsetSum.Counting.GuessArrayExecution |
|
|
| namespace OAI |
|
|
| /-! # Three actual interval draws and their stored guess array -/ |
|
|
| noncomputable section |
| namespace LowSpaceSubsetSum.GuessSamplerCells |
|
|
| def one (n : ℕ) (s : (CanonicalGuesses.coupling n).Seed) : |
| SamplerExecution.Trace ↥(RepresentationSetup.guessRange n) × ℕ := |
| let r := SamplerFinCells.run n (CanonicalGuesses.width n) s |
| (⟨r.1.value.map (CanonicalGuesses.encoding n), r.1.reads, r.1.tests⟩, r.2+8) |
|
|
| theorem one_value (n : ℕ) (s : (CanonicalGuesses.coupling n).Seed) : |
| (one n s).1 = (CanonicalGuesses.execution n).run s := by |
| have h := SamplerFinCells.run_value n (CanonicalGuesses.width n) s |
| simp only [one, CanonicalGuesses.execution, SamplerExecution.map] |
| rw [h] |
|
|
| theorem one_cells (n : ℕ) (s : (CanonicalGuesses.coupling n).Seed) : |
| (one n s).2 ≤ 3*n^3+88 := by |
| have h := SamplerFinCells.run_cells n (CanonicalGuesses.width n) s |
| change _+8 ≤ _ |
| omega |
|
|
| def trace (n : ℕ) (s : (GuessArrayExecution.coupling n).Seed) := |
| SamplerPiCells.run 3 (fun _ => ↥(RepresentationSetup.guessRange n)) |
| (fun _ => CanonicalGuesses.coupling n) (fun _ => one n) (fun _ => 3*n^3+88) s |
|
|
| theorem trace_value (n : ℕ) (s : (GuessArrayExecution.coupling n).Seed) : |
| (trace n s).1 = (GuessArrayExecution.execution n).run s := |
| SamplerPiCells.value 3 _ _ _ _ (fun _ => CanonicalGuesses.execution n) (fun _ => one_value n) s |
|
|
| theorem trace_cells (n : ℕ) (s : (GuessArrayExecution.coupling n).Seed) : |
| (trace n s).2 ≤ 9*n^3+344 := by |
| have h := SamplerPiCells.cells 3 (fun _ => ↥(RepresentationSetup.guessRange n)) |
| (fun _ => CanonicalGuesses.coupling n) (fun _ => one n) (fun _ => 3*n^3+88) |
| (fun _ => one_cells n) s |
| simp only [Finset.sum_const, Finset.card_univ, Fintype.card_fin, smul_eq_mul] at h |
| dsimp only [trace] |
| omega |
|
|
| def run (n : ℕ) (s : (GuessArrayExecution.coupling n).Seed) : |
| (Option (Vector ℕ 3) × ℕ) × ℕ := |
| let r := trace n s |
| ((r.1.value.map (fun g => Vector.ofFn (fun i => (g i).val)), r.1.reads+r.1.tests+7), r.2+16) |
|
|
| theorem run_value (n : ℕ) (s : (GuessArrayExecution.coupling n).Seed) : |
| (run n s).1 = GuessArrayExecution.run n s := by |
| simp only [run, trace_value, GuessArrayExecution.run] |
|
|
| theorem run_cells (n : ℕ) (s : (GuessArrayExecution.coupling n).Seed) : |
| (run n s).2 ≤ 9*n^3+360 := by |
| have h := trace_cells n s |
| change _+16 ≤ _ |
| omega |
|
|
| end LowSpaceSubsetSum.GuessSamplerCells |
|
|
| end |
|
|
| end OAI |
|
|
