File size: 1,662 Bytes
e5a97c6 | 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 | import OAI.Combinatorics.LowSpaceSubsetSum.Word.WordSeedHistoryExecution
import OAI.Combinatorics.LowSpaceSubsetSum.Word.WordSeedSeparatorPreparation
import OAI.Combinatorics.LowSpaceSubsetSum.Word.WordSamplingBounds
namespace OAI
/-! # Executed separator families complete the representation history -/
noncomputable section
namespace LowSpaceSubsetSum.WordSeedMeasured
variable {n : ℕ}
private theorem clog_le (k w : ℕ) (h : k ≤ w) : Nat.clog 2 k ≤ w :=
(Nat.clog_le_of_le_pow Nat.lt_two_pow_self.le).trans h
def separatorDraws (R : RepresentationSetup n) (h : R.PrimeHistory)
(hn : 2200 ≤ n) (w : ℕ)
(hw : Nat.clog 2 (2*RepresentationSetup.blockHalf n 0) ≤ w) :
Execution (WordSeedRealization.separatorDraws R h hn w hw) := by
unfold WordSeedRealization.separatorDraws RepresentationSetup.separatorParameters
exact familiesPrepared _ _ _ _ _ _ w n hw
def bucketHistory (I : Instance n) (hn : 10000 ≤ n) (w : ℕ) (hw : 3*n+1 ≤ w) :
Execution (WordSeedRealization.bucketHistory (canonicalRepresentationData I).zeroSetup hn w hw) :=
bind (extraHistory I (by omega) w hw)
(fun h => (canonicalRepresentationData I).zeroSetup.SeparatorDraws h.1.1 (by omega))
(fun h => (canonicalRepresentationData I).zeroSetup.separatorCoupling h.1.1 (by omega))
(fun h => WordSeedRealization.separatorDraws _ h.1.1 (by omega) w
(clog_le _ _ (by
have hg := WordSamplingBounds.family_width n
omega)))
(fun h => separatorDraws _ h.1.1 (by omega) w
(clog_le _ _ (by
have hg := WordSamplingBounds.family_width n
omega)))
end LowSpaceSubsetSum.WordSeedMeasured
end
end OAI
|