File size: 3,325 Bytes
e63eb7f | 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.EditApproximation.Queries.QueryChargedFamily
import OAI.Combinatorics.EditApproximation.Queries.QueryWarmupWidth
import OAI.Combinatorics.EditApproximation.Queries.QueryBoundedActiveCost
namespace OAI
namespace EditApproximation
open BinaryFraction
section Table
variable {M J R passes copies T S : ℕ} [NeZero M] [NeZero R]
(source target : List ℕ) (N P F exponent H Q eM eF B : ℕ)
(hP : 0 < P) (hM : M = 2 ^ eM) (hF : F = 2 ^ eF)
(A a : ℕ → BinaryFraction) (tau eta kappa delta : BinaryFraction) (multiplier : ℕ → ℕ)
(occurrence : BinaryMemo PositionCounts) (symbolBits positionBits : ℕ)
(parent : {r : PhysicalTableRequest M J target.length // r.Bounded (passes + 1) copies T S})
(oracle : ChargedFamilyQueryKey (R := R) target N P F exponent H Q (.inr parent) → BinaryFraction)
theorem queryChargedFamilyTable_width
(hB : 10 ≤ B) (hN : Nat.size N ≤ B) (hPb : Nat.size P ≤ B)
(hFb : Nat.size F + 2 ≤ B) (hFpos : 1 ≤ F)
(hs : Nat.size source.length + 2 ≤ B) (ht : Nat.size target.length + 2 ≤ B)
(ht' : Nat.size (target.length + 1) + 2 ≤ B)
(hinit : Nat.size ((32 * F + 1) * N) + 3 ≤ B)
(hMb : Nat.size M ≤ B) (ha : (a parent.val.pass).width ≤ B)
(hv : ∀ key, (oracle (Sum.inr key)).width ≤ B)
(hactive : ∀ (hindex : T < parent.val.index) (hbelow : parent.val.node.1.val < J),
((queryFamilyBoundedActive (R := R) source target N P F exponent H Q eM eF hP hM hF
tau (a parent.val.pass) eta kappa delta T S passes copies parent hindex hbelow).value
(fun key => oracle (Sum.map id (fun child =>
⟨Sum.inr child.val, ChargedPhysicalRequest.table_rank_lt parent child.val child.property⟩) key))).width ≤
preparedKernelWordBudget M B) :
((queryChargedFamilyTable (R := R) source target N P F exponent H Q eM eF hP hM hF A a tau eta kappa
delta multiplier occurrence symbolBits positionBits parent).value oracle).width ≤
localWarmupWordBudget M B + preparedKernelWordBudget M B := by
let tableOracle := fun key => oracle (Sum.inr key)
have hw := queryChargedWarmup_width source target N P F B (A parent.val.pass) (a parent.val.pass)
multiplier parent occurrence symbolBits positionBits tableOracle hB hP hN hPb hFb hFpos hs ht ht'
hinit hMb ha hv
have hi := queryPhysicalInitial_width source target N P F B (A parent.val.pass) (a parent.val.pass)
multiplier parent occurrence symbolBits positionBits tableOracle parent.val.state hP ht' hinit
have hsmall : B ≤ localWarmupWordBudget M B := by
unfold localWarmupWordBudget physicalContinuationInputBudget
dsimp only
omega
unfold queryChargedFamilyTable
simp only [BitQuery.value]
split
· simp only [BitQuery.mapKeysWithWork_value]
exact hw.trans (Nat.le_add_right _ _)
· split
· split
· simp only [BitQuery.value, BitQuery.mapKeysWithWork_value]
exact hi.trans (hsmall.trans (Nat.le_add_right _ _))
· rename_i hindex hbelow hlong
simp only [BitQuery.value, BitQuery.mapKeysWithWork_value]
exact (hactive _ _).trans (Nat.le_add_left _ _)
· simp only [BitQuery.value, BitQuery.mapKeysWithWork_value]
exact hi.trans (hsmall.trans (Nat.le_add_right _ _))
end Table
end EditApproximation
end OAI
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