| import OAI.Combinatorics.EditApproximation.Geometry.ComparisonLift |
| import OAI.Combinatorics.EditApproximation.Refinement.StageTerminal |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalRefinementSpatial |
| import OAI.Combinatorics.EditApproximation.Numerics.RationalWideSpatial |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalRefinementInvariants |
| import OAI.Combinatorics.EditApproximation.Refinement.ComputedBandSpacing |
| import OAI.Combinatorics.EditApproximation.Geometry.UnskippedBands |
| import OAI.Combinatorics.EditApproximation.Numerics.RationalWideStep |
| import OAI.Combinatorics.EditApproximation.Refinement.StageComparison |
| import OAI.Combinatorics.EditApproximation.Geometry.OnlineActionDraw |
| import OAI.Combinatorics.EditApproximation.Geometry.ComparisonPhysical |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalLeaves |
| import OAI.Combinatorics.EditApproximation.Refinement.ComputedComparisonBand |
| import OAI.Combinatorics.EditApproximation.Geometry.BandRounding |
| import OAI.Combinatorics.EditApproximation.Geometry.BandEnvelopes |
| import OAI.Combinatorics.EditApproximation.Geometry.BandGuards |
| import OAI.Combinatorics.EditApproximation.Refinement.StageWarmup |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSpatial |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalWarmupSlack |
| import OAI.Combinatorics.EditApproximation.Geometry.BandParameters |
| import OAI.Combinatorics.EditApproximation.Geometry.ComparisonBandCoverage |
| import OAI.Combinatorics.EditApproximation.Geometry.RepresentativeBands |
| import OAI.Combinatorics.EditApproximation.Geometry.PrefixComparison |
| import OAI.Combinatorics.EditApproximation.Refinement.ComputedBands |
| import OAI.Combinatorics.EditApproximation.Geometry.InitialSeedTable |
| import OAI.Combinatorics.EditApproximation.Geometry.ComparisonParameters |
| import OAI.Combinatorics.EditApproximation.Numerics.RationalPrefix |
| import OAI.Combinatorics.EditApproximation.Coarse.CoarseArrayEval |
| import OAI.Combinatorics.EditApproximation.Coarse.CoarseGlobalSeed |
| import OAI.Combinatorics.EditApproximation.Geometry.WideBellman |
| import OAI.Combinatorics.EditApproximation.Geometry.PrefixCosts |
| import OAI.Combinatorics.EditApproximation.Geometry.ComparisonBounds |
| import OAI.Combinatorics.EditApproximation.Geometry.StateDomain |
| import OAI.Combinatorics.EditApproximation.Geometry.SharedActions |
| import OAI.Combinatorics.EditApproximation.Geometry.SourcePrefixes |
| import OAI.Combinatorics.EditApproximation.Geometry.ComparisonTree |
| import OAI.Combinatorics.EditApproximation.Geometry.RoundedComparison |
| import OAI.Combinatorics.EditApproximation.Refinement.ComputedSeed |
| import OAI.Combinatorics.EditApproximation.Coarse.CoarseParameters |
| import OAI.Combinatorics.EditApproximation.Coarse.CoarsePrecision |
| import OAI.Combinatorics.EditApproximation.Coarse.CoarseInitialWork |
| import OAI.Combinatorics.EditApproximation.Geometry.Accuracy |
| import OAI.Combinatorics.EditApproximation.Probability.Amplification |
| import OAI.Combinatorics.EditApproximation.Geometry.ActionLower |
| import OAI.Combinatorics.EditApproximation.Geometry.ActionVectors |
| import OAI.Combinatorics.EditApproximation.Geometry.ActualActionValues |
| import OAI.Combinatorics.EditApproximation.Geometry.AlignedStates |
| import OAI.Combinatorics.EditApproximation.Geometry.AlignmentSplitting |
| import OAI.Combinatorics.EditApproximation.Geometry.Bands |
| import OAI.Combinatorics.EditApproximation.Geometry.Bellman |
| import OAI.Combinatorics.EditApproximation.Geometry.BandRegret |
| import OAI.Combinatorics.EditApproximation.Geometry.BalancedIntervals |
| import OAI.Combinatorics.EditApproximation.Geometry.BalancedWidths |
| import OAI.Combinatorics.EditApproximation.Geometry.ChildIncrements |
| import OAI.Combinatorics.EditApproximation.Coarse.CoarseAccuracy |
| import OAI.Combinatorics.EditApproximation.Coarse.CoarseEstimator |
| import OAI.Combinatorics.EditApproximation.Coarse.CoarseSampling |
| import OAI.Combinatorics.EditApproximation.Coarse.CoarseProbability |
| import OAI.Combinatorics.EditApproximation.Coarse.CoarseTransforms |
| import OAI.Combinatorics.EditApproximation.Coarse.CoarseWork |
| import OAI.Combinatorics.EditApproximation.Coarse.CoarsePadding |
| import OAI.Combinatorics.EditApproximation.Coarse.CoarseInitial |
| import OAI.Combinatorics.EditApproximation.Coarse.CoarseSeed |
| import OAI.Combinatorics.EditApproximation.Geometry.ComparisonAccounting |
| import OAI.Combinatorics.EditApproximation.Probability.Concentration |
| import OAI.Combinatorics.EditApproximation.Geometry.Cones |
| import OAI.Combinatorics.EditApproximation.Geometry.ConeLocality |
| import OAI.Combinatorics.EditApproximation.Geometry.Connections |
| import OAI.Combinatorics.EditApproximation.Geometry.Curvature |
| import OAI.Combinatorics.EditApproximation.Geometry.DomainCounts |
| import OAI.Combinatorics.EditApproximation.Geometry.DomainExponential |
| import OAI.Combinatorics.EditApproximation.Probability.Exact |
| import OAI.Combinatorics.EditApproximation.Probability.ExactSampling |
| import OAI.Combinatorics.EditApproximation.Probability.ExpectedRegret |
| import OAI.Combinatorics.EditApproximation.Geometry.FirstCrossing |
| import OAI.Combinatorics.EditApproximation.Probability.FiniteAssignments |
| import OAI.Combinatorics.EditApproximation.Geometry.GroupSampling |
| import OAI.Combinatorics.EditApproximation.Geometry.Grid |
| import OAI.Combinatorics.EditApproximation.Geometry.Leaves |
| import OAI.Combinatorics.EditApproximation.Geometry.LocalGrid |
| import OAI.Combinatorics.EditApproximation.Geometry.LocalInitialCones |
| import OAI.Combinatorics.EditApproximation.Geometry.InitialCones |
| import OAI.Combinatorics.EditApproximation.Geometry.InitialConeGrid |
| import OAI.Combinatorics.EditApproximation.Geometry.InitialConeTable |
| import OAI.Combinatorics.EditApproximation.Probability.Median |
| import OAI.Combinatorics.EditApproximation.Numerics.Numerics |
| import OAI.Combinatorics.EditApproximation.Numerics.NumericalWork |
| import OAI.Combinatorics.EditApproximation.Geometry.NodeRegret |
| import OAI.Combinatorics.EditApproximation.Geometry.ParameterSlack |
| import OAI.Combinatorics.EditApproximation.Geometry.Parameters |
| import OAI.Combinatorics.EditApproximation.Geometry.PartitionIntervals |
| import OAI.Combinatorics.EditApproximation.Numerics.RationalRefinement |
| import OAI.Combinatorics.EditApproximation.Probability.SampledRegret |
| import OAI.Combinatorics.EditApproximation.Geometry.StateGeometry |
| import OAI.Combinatorics.EditApproximation.Probability.ThresholdMoments |
| import OAI.Combinatorics.EditApproximation.Geometry.TreeAccounting |
| import OAI.Combinatorics.EditApproximation.Geometry.TreeParameters |
| import OAI.Combinatorics.EditApproximation.Geometry.Work |
| import OAI.Combinatorics.EditApproximation.Geometry.WeightedTreeWork |
| import OAI.Combinatorics.EditApproximation.Geometry.WideActions |
| import OAI.Combinatorics.EditApproximation.Geometry.BandGroupSampling |
| import OAI.Combinatorics.EditApproximation.Geometry.CellGroupSelection |
| import OAI.Combinatorics.EditApproximation.Geometry.ComparisonLiftBounds |
| import OAI.Combinatorics.EditApproximation.Refinement.ComputedGroupAccuracy |
| import OAI.Combinatorics.EditApproximation.Refinement.ComputedGroupNumerical |
| import OAI.Combinatorics.EditApproximation.Geometry.GroupCells |
| import OAI.Combinatorics.EditApproximation.Geometry.GroupNumerical |
| import OAI.Combinatorics.EditApproximation.Geometry.GroupSmallConstants |
| import OAI.Combinatorics.EditApproximation.Geometry.ListBandRegret |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalGroupAccuracy |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalOnlineBand |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalNodeRegret |
| import OAI.Combinatorics.EditApproximation.Refinement.StageComparisonEnergy |
| import OAI.Combinatorics.EditApproximation.Refinement.StageParameterBounds |
|
|
| import OAI.Combinatorics.EditApproximation.Geometry.ComparisonLiftStep |
| import OAI.Combinatorics.EditApproximation.Refinement.StageComparisonCharges |
| import OAI.Combinatorics.EditApproximation.Refinement.StageComparisonBad |
| import OAI.Combinatorics.EditApproximation.Geometry.BandDimension |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalUnskippedComparison |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalTreeRegret |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalGenericRegret |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalComparisonBand |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalTreeGeneric |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalTreeExpectation |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalExpectedRegret |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalParentDraw |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalRefinementLocality |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalResampledRegret |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalConditionalNode |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSelectionProgram |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSelectionResampling |
| import OAI.Combinatorics.EditApproximation.Probability.FiniteResampling |
| import OAI.Combinatorics.EditApproximation.Refinement.StageComparisonPrediction |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalTreeNear |
| import OAI.Combinatorics.EditApproximation.Geometry.UnskippedRegretBudget |
| import OAI.Combinatorics.EditApproximation.Refinement.ComputedStageParameters |
| import OAI.Combinatorics.EditApproximation.Refinement.ComputedStageTime |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalBoundsAllSeeds |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalTreeBudget |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramLaw |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramRefreshWiring |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramNodeRegret |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramComparisonRegret |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramAccuracy |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalOnlineLocality |
| import OAI.Combinatorics.EditApproximation.Geometry.RefinementErrorTerms |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalDenominator |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalValueBits |
| import OAI.Combinatorics.EditApproximation.Numerics.RationalPruning |
| import OAI.Combinatorics.EditApproximation.Geometry.RefinementConeLocality |
| import OAI.Combinatorics.EditApproximation.Geometry.LocalCells |
| import OAI.Combinatorics.EditApproximation.Geometry.LocalRefinementCones |
| import OAI.Combinatorics.EditApproximation.Geometry.GroupSamplingWork |
| import OAI.Combinatorics.EditApproximation.Geometry.LocalGroupCones |
| import OAI.Combinatorics.EditApproximation.Geometry.RoundedGroupStates |
| import OAI.Combinatorics.EditApproximation.Geometry.DyadicQueryWindow |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtree |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeMass |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeCharges |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeRegret |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeExpectation |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeBad |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeGeneric |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreePrediction |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeNear |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeBudget |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramSubtreeRegret |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramStateAccuracy |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSeedMedian |
| import OAI.Combinatorics.EditApproximation.Geometry.ActualRoundedGroupInputs |
| import OAI.Combinatorics.EditApproximation.Geometry.SharedGroupInputBudget |
| import OAI.Combinatorics.EditApproximation.Geometry.SeedPassNumerics |
| import OAI.Combinatorics.EditApproximation.Geometry.SeedFactorSchedule |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalQueryBudget |
| import OAI.Combinatorics.EditApproximation.Geometry.LocalGroupBudget |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSeedPass |
| import OAI.Combinatorics.EditApproximation.Probability.AdaptiveSeedLaw |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSeedTables |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalSeedSchedule |
| import OAI.Combinatorics.EditApproximation.Binary.BinaryMemo |
| import OAI.Combinatorics.EditApproximation.Geometry.CurrentQueryInputs |
| import OAI.Combinatorics.EditApproximation.Geometry.GroupInputDependence |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalLocalGroupProgram |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalLocalWarmup |
| import OAI.Combinatorics.EditApproximation.Probability.FiniteSeedFinal |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalCoarseSeedLaw |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalFinalAccuracy |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalConditionalAccuracy |
| import OAI.Combinatorics.EditApproximation.Geometry.LocalWideStep |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalLocalRefinement |
| import OAI.Combinatorics.EditApproximation.Refinement.PhysicalLocalRefinementEquality |
| import OAI.Combinatorics.EditApproximation.Refinement.ComputedCurrentQueryBudget |
|
|
| import OAI.Combinatorics.EditApproximation.AlmostLinear |
|
|
| /-! |
| # Almost-linear approximation of edit distance |
|
|
| A uniform binary randomized approximation scheme attains success probability |
| at least two thirds, returns zero on equal strings, uses almost-linear expected |
| work for each fixed binary accuracy, and has polynomial space on every outcome. |
| Finite Bernstein concentration discharges the hypotheses of its conditional |
| accuracy and work bounds. |
| -/ |
|
|
