File size: 2,566 Bytes
5d5048e | 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 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 | 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
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