| import OAI.Combinatorics.EditApproximation.Specification.RawBandPipelineFootprintBridges |
| import OAI.Combinatorics.EditApproximation.Definitions |
|
|
| namespace OAI.EditApproximation |
| open Filter MeasureTheory |
| attribute [local instance] queryRoundsNeZero |
|
|
| theorem almostLinearEditDistanceRawBand (epsilon : BinaryFraction) |
| (hepsilon : 0 < epsilon.value) (_hepsilonOne : epsilon.value < 1) |
| : |
| (∀ (source target : List ℤ) (N : ℕ), source.length + target.length ≤ N → |
| (2 / 3 : ℝ) ≤ (computedFullLaw (source.map integerSymbolCode) (target.map integerSymbolCode) N epsilon).real |
| {outcome | EditDistortion.edit source target ≤ integerBinaryAnswerRawBand source target N epsilon outcome ∧ |
| (integerBinaryAnswerRawBand source target N epsilon outcome : ℝ) ≤ |
| (1 + (epsilon.value : ℝ)) * EditDistortion.edit source target}) ∧ |
| (∀ (source target : List ℤ) (N : ℕ), source = target → ∀ outcome, |
| integerBinaryAnswerRawBand source target N epsilon outcome = 0) ∧ |
| (∀ (C : ℕ) (eta : ℝ), 0 < eta → ∀ᶠ N : ℕ in atTop, |
| ∀ source target : List ℤ, source.length + target.length ≤ N → |
| (∀ z ∈ source ++ target, z.natAbs ≤ (N + 2) ^ C) → |
| (∫ outcome, integerBinaryWorkRawBand source target N epsilon outcome |
| ∂computedFullLaw (source.map integerSymbolCode) (target.map integerSymbolCode) N epsilon) ≤ |
| (N + 2 : ℝ) ^ (1 + eta)) ∧ |
| (∀ C : ℕ, ∀ᶠ N : ℕ in atTop, ∀ source target : List ℤ, |
| source.length + target.length ≤ N → |
| (∀ z ∈ source ++ target, z.natAbs ≤ (N + 2) ^ C) → |
| ∀ outcome, integerBinarySpaceFootprintRawBand source target N epsilon outcome ≤ (N + 2) ^ (C + 65564)) := by |
| simpa only [integerBinaryAnswerRawBand_eq, integerBinaryWorkRawBand_eq, |
| integerBinarySpaceFootprintRawBand_eq] using |
| almostLinearEditDistance_main epsilon hepsilon _hepsilonOne |
|
|
| end OAI.EditApproximation |
|
|
