File size: 3,000 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.QueryFamilyScalarReads
import OAI.Combinatorics.EditApproximation.Queries.QueryPhysicalSourceCosts
namespace OAI
namespace EditApproximation
section Family
variable {α : Type*} {M J R : ℕ} (target : List α)
(N P F exponent H Q passes copies pass copy : ℕ)
theorem queryFamilyTagWithWork_cost (B : ℕ)
(hp : Nat.size pass ≤ B) (hc : Nat.size copy ≤ B)
(hps : Nat.size (passes + 1) ≤ B) (hcs : Nat.size (copies + 1) ≤ B)
(scalar : PhysicalScalarKey M J N target.length exponent F Q R (localOnlineMassBound M P H)) :
(queryFamilyTagWithWork target N P F exponent H Q passes copies pass copy scalar).2 ≤
120 * (B + 1) ^ 2 + 5 * J + 55 := by
have h1 := queryFinOfNatWithWork_cost (passes + 1) pass B (Nat.succ_pos _) hps hp
have h2 := queryFinOfNatWithWork_cost (copies + 1) copy B (Nat.succ_pos _) hcs hc
have h3 := physicalFamilyCodeWithWork_cost target N P F exponent H Q passes copies
((queryFinOfNatWithWork (passes + 1) pass (Nat.succ_pos _)).1,
(queryFinOfNatWithWork (copies + 1) copy (Nat.succ_pos _)).1, scalar)
change (queryFinOfNatWithWork (passes + 1) pass (Nat.succ_pos _)).2 +
(queryFinOfNatWithWork (copies + 1) copy (Nat.succ_pos _)).2 + _ + 1 ≤ _
omega
variable
(oracle : PhysicalFamilyScalarKey (M := M) (J := J) (R := R)
target N P F exponent H Q passes copies → BinaryFraction)
(readWork : PhysicalFamilyScalarKey (M := M) (J := J) (R := R)
target N P F exponent H Q passes copies → ℕ)
(K W : ℕ)
(hK : ∀ scalar : PhysicalScalarKey M J N target.length exponent F Q R (localOnlineMassBound M P H),
(queryFamilyTagWithWork target N P F exponent H Q passes copies pass copy scalar).2 ≤ K)
(hW : ∀ key, readWork key ≤ W)
include hK hW in
theorem queryFamilyGroupRead_work (node : PhysicalInternalNode M J) (time : Fin R)
(key : GroupScalarKey M F Q) :
(queryFamilyGroupRead target N P F exponent H Q passes copies pass copy node time key).work
oracle readWork ≤ (queryScalePresentWithWork N key.1.1).2 +
(queryCellValidWithWork target.length exponent key.1.2).2 + 5 * J + 43 + (K + W) := by
unfold queryFamilyGroupRead
rw [BitQuery.mapKeysWithWork_work]
apply queryPhysicalScalarGroupRead_work
intro scalar
exact Nat.add_le_add (hK scalar) (hW _)
include hK hW in
theorem queryFamilyOnlineRead_work (node : PhysicalInternalNode M J) (time : Fin R)
(key : ℕ × TargetInterval target.length) (range : ℕ) :
(queryFamilyOnlineRead target N P F exponent H Q passes copies pass copy node time key range).work
oracle readWork ≤ (queryScalePresentWithWork N key.1).2 +
(queryRangeValidWithWork (localOnlineMassBound M P H) range).2 + 5 * J + 43 + (K + W) := by
unfold queryFamilyOnlineRead
rw [BitQuery.mapKeysWithWork_work]
apply queryPhysicalScalarOnlineRead_work
intro scalar
exact Nat.add_le_add (hK scalar) (hW _)
end Family
end EditApproximation
end OAI
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