OAI/Combinatorics/EditApproximation/BasicResults.lean
0 declarations, 0 contain sorry, 0 declared as axioms
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.
This file declares nothing itself. It gathers the 193 imports below, so a file that imports it gets all of them.
Imports
- OAI.Combinatorics.EditApproximation.Geometry.ComparisonLift
- OAI.Combinatorics.EditApproximation.Refinement.StageTerminal
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalRefinementSpatial
- OAI.Combinatorics.EditApproximation.Numerics.RationalWideSpatial
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalRefinementInvariants
- OAI.Combinatorics.EditApproximation.Refinement.ComputedBandSpacing
- OAI.Combinatorics.EditApproximation.Geometry.UnskippedBands
- OAI.Combinatorics.EditApproximation.Numerics.RationalWideStep
- OAI.Combinatorics.EditApproximation.Refinement.StageComparison
- OAI.Combinatorics.EditApproximation.Geometry.OnlineActionDraw
- OAI.Combinatorics.EditApproximation.Geometry.ComparisonPhysical
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalLeaves
- OAI.Combinatorics.EditApproximation.Refinement.ComputedComparisonBand
- OAI.Combinatorics.EditApproximation.Geometry.BandRounding
- OAI.Combinatorics.EditApproximation.Geometry.BandEnvelopes
- OAI.Combinatorics.EditApproximation.Geometry.BandGuards
- OAI.Combinatorics.EditApproximation.Refinement.StageWarmup
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSpatial
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalWarmupSlack
- OAI.Combinatorics.EditApproximation.Geometry.BandParameters
- OAI.Combinatorics.EditApproximation.Geometry.ComparisonBandCoverage
- OAI.Combinatorics.EditApproximation.Geometry.RepresentativeBands
- OAI.Combinatorics.EditApproximation.Geometry.PrefixComparison
- OAI.Combinatorics.EditApproximation.Refinement.ComputedBands
- OAI.Combinatorics.EditApproximation.Geometry.InitialSeedTable
- OAI.Combinatorics.EditApproximation.Geometry.ComparisonParameters
- OAI.Combinatorics.EditApproximation.Numerics.RationalPrefix
- OAI.Combinatorics.EditApproximation.Coarse.CoarseArrayEval
- OAI.Combinatorics.EditApproximation.Coarse.CoarseGlobalSeed
- OAI.Combinatorics.EditApproximation.Geometry.WideBellman
- OAI.Combinatorics.EditApproximation.Geometry.PrefixCosts
- OAI.Combinatorics.EditApproximation.Geometry.ComparisonBounds
- OAI.Combinatorics.EditApproximation.Geometry.StateDomain
- OAI.Combinatorics.EditApproximation.Geometry.SharedActions
- OAI.Combinatorics.EditApproximation.Geometry.SourcePrefixes
- OAI.Combinatorics.EditApproximation.Geometry.ComparisonTree
- OAI.Combinatorics.EditApproximation.Geometry.RoundedComparison
- OAI.Combinatorics.EditApproximation.Refinement.ComputedSeed
- OAI.Combinatorics.EditApproximation.Coarse.CoarseParameters
- OAI.Combinatorics.EditApproximation.Coarse.CoarsePrecision
- OAI.Combinatorics.EditApproximation.Coarse.CoarseInitialWork
- OAI.Combinatorics.EditApproximation.Geometry.Accuracy
- OAI.Combinatorics.EditApproximation.Probability.Amplification
- OAI.Combinatorics.EditApproximation.Geometry.ActionLower
- OAI.Combinatorics.EditApproximation.Geometry.ActionVectors
- OAI.Combinatorics.EditApproximation.Geometry.ActualActionValues
- OAI.Combinatorics.EditApproximation.Geometry.AlignedStates
- OAI.Combinatorics.EditApproximation.Geometry.AlignmentSplitting
- OAI.Combinatorics.EditApproximation.Geometry.Bands
- OAI.Combinatorics.EditApproximation.Geometry.Bellman
- OAI.Combinatorics.EditApproximation.Geometry.BandRegret
- OAI.Combinatorics.EditApproximation.Geometry.BalancedIntervals
- OAI.Combinatorics.EditApproximation.Geometry.BalancedWidths
- OAI.Combinatorics.EditApproximation.Geometry.ChildIncrements
- OAI.Combinatorics.EditApproximation.Coarse.CoarseAccuracy
- OAI.Combinatorics.EditApproximation.Coarse.CoarseEstimator
- OAI.Combinatorics.EditApproximation.Coarse.CoarseSampling
- OAI.Combinatorics.EditApproximation.Coarse.CoarseProbability
- OAI.Combinatorics.EditApproximation.Coarse.CoarseTransforms
- OAI.Combinatorics.EditApproximation.Coarse.CoarseWork
- OAI.Combinatorics.EditApproximation.Coarse.CoarsePadding
- OAI.Combinatorics.EditApproximation.Coarse.CoarseInitial
- OAI.Combinatorics.EditApproximation.Coarse.CoarseSeed
- OAI.Combinatorics.EditApproximation.Geometry.ComparisonAccounting
- OAI.Combinatorics.EditApproximation.Probability.Concentration
- OAI.Combinatorics.EditApproximation.Geometry.Cones
- OAI.Combinatorics.EditApproximation.Geometry.ConeLocality
- OAI.Combinatorics.EditApproximation.Geometry.Connections
- OAI.Combinatorics.EditApproximation.Geometry.Curvature
- OAI.Combinatorics.EditApproximation.Geometry.DomainCounts
- OAI.Combinatorics.EditApproximation.Geometry.DomainExponential
- OAI.Combinatorics.EditApproximation.Probability.Exact
- OAI.Combinatorics.EditApproximation.Probability.ExactSampling
- OAI.Combinatorics.EditApproximation.Probability.ExpectedRegret
- OAI.Combinatorics.EditApproximation.Geometry.FirstCrossing
- OAI.Combinatorics.EditApproximation.Probability.FiniteAssignments
- OAI.Combinatorics.EditApproximation.Geometry.GroupSampling
- OAI.Combinatorics.EditApproximation.Geometry.Grid
- OAI.Combinatorics.EditApproximation.Geometry.Leaves
- OAI.Combinatorics.EditApproximation.Geometry.LocalGrid
- OAI.Combinatorics.EditApproximation.Geometry.LocalInitialCones
- OAI.Combinatorics.EditApproximation.Geometry.InitialCones
- OAI.Combinatorics.EditApproximation.Geometry.InitialConeGrid
- OAI.Combinatorics.EditApproximation.Geometry.InitialConeTable
- OAI.Combinatorics.EditApproximation.Probability.Median
- OAI.Combinatorics.EditApproximation.Numerics.Numerics
- OAI.Combinatorics.EditApproximation.Numerics.NumericalWork
- OAI.Combinatorics.EditApproximation.Geometry.NodeRegret
- OAI.Combinatorics.EditApproximation.Geometry.ParameterSlack
- OAI.Combinatorics.EditApproximation.Geometry.Parameters
- OAI.Combinatorics.EditApproximation.Geometry.PartitionIntervals
- OAI.Combinatorics.EditApproximation.Numerics.RationalRefinement
- OAI.Combinatorics.EditApproximation.Probability.SampledRegret
- OAI.Combinatorics.EditApproximation.Geometry.StateGeometry
- OAI.Combinatorics.EditApproximation.Probability.ThresholdMoments
- OAI.Combinatorics.EditApproximation.Geometry.TreeAccounting
- OAI.Combinatorics.EditApproximation.Geometry.TreeParameters
- OAI.Combinatorics.EditApproximation.Geometry.Work
- OAI.Combinatorics.EditApproximation.Geometry.WeightedTreeWork
- OAI.Combinatorics.EditApproximation.Geometry.WideActions
- OAI.Combinatorics.EditApproximation.Geometry.BandGroupSampling
- OAI.Combinatorics.EditApproximation.Geometry.CellGroupSelection
- OAI.Combinatorics.EditApproximation.Geometry.ComparisonLiftBounds
- OAI.Combinatorics.EditApproximation.Refinement.ComputedGroupAccuracy
- OAI.Combinatorics.EditApproximation.Refinement.ComputedGroupNumerical
- OAI.Combinatorics.EditApproximation.Geometry.GroupCells
- OAI.Combinatorics.EditApproximation.Geometry.GroupNumerical
- OAI.Combinatorics.EditApproximation.Geometry.GroupSmallConstants
- OAI.Combinatorics.EditApproximation.Geometry.ListBandRegret
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalGroupAccuracy
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalOnlineBand
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalNodeRegret
- OAI.Combinatorics.EditApproximation.Refinement.StageComparisonEnergy
- OAI.Combinatorics.EditApproximation.Refinement.StageParameterBounds
- OAI.Combinatorics.EditApproximation.Geometry.ComparisonLiftStep
- OAI.Combinatorics.EditApproximation.Refinement.StageComparisonCharges
- OAI.Combinatorics.EditApproximation.Refinement.StageComparisonBad
- OAI.Combinatorics.EditApproximation.Geometry.BandDimension
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalUnskippedComparison
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalTreeRegret
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalGenericRegret
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalComparisonBand
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalTreeGeneric
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalTreeExpectation
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalExpectedRegret
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalParentDraw
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalRefinementLocality
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalResampledRegret
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalConditionalNode
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSelectionProgram
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSelectionResampling
- OAI.Combinatorics.EditApproximation.Probability.FiniteResampling
- OAI.Combinatorics.EditApproximation.Refinement.StageComparisonPrediction
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalTreeNear
- OAI.Combinatorics.EditApproximation.Geometry.UnskippedRegretBudget
- OAI.Combinatorics.EditApproximation.Refinement.ComputedStageParameters
- OAI.Combinatorics.EditApproximation.Refinement.ComputedStageTime
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalBoundsAllSeeds
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalTreeBudget
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramLaw
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramRefreshWiring
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramNodeRegret
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramComparisonRegret
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramAccuracy
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalOnlineLocality
- OAI.Combinatorics.EditApproximation.Geometry.RefinementErrorTerms
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalDenominator
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalValueBits
- OAI.Combinatorics.EditApproximation.Numerics.RationalPruning
- OAI.Combinatorics.EditApproximation.Geometry.RefinementConeLocality
- OAI.Combinatorics.EditApproximation.Geometry.LocalCells
- OAI.Combinatorics.EditApproximation.Geometry.LocalRefinementCones
- OAI.Combinatorics.EditApproximation.Geometry.GroupSamplingWork
- OAI.Combinatorics.EditApproximation.Geometry.LocalGroupCones
- OAI.Combinatorics.EditApproximation.Geometry.RoundedGroupStates
- OAI.Combinatorics.EditApproximation.Geometry.DyadicQueryWindow
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtree
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeMass
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeCharges
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeRegret
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeExpectation
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeBad
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeGeneric
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreePrediction
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeNear
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSubtreeBudget
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramSubtreeRegret
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalProgramStateAccuracy
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSeedMedian
- OAI.Combinatorics.EditApproximation.Geometry.ActualRoundedGroupInputs
- OAI.Combinatorics.EditApproximation.Geometry.SharedGroupInputBudget
- OAI.Combinatorics.EditApproximation.Geometry.SeedPassNumerics
- OAI.Combinatorics.EditApproximation.Geometry.SeedFactorSchedule
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalQueryBudget
- OAI.Combinatorics.EditApproximation.Geometry.LocalGroupBudget
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSeedPass
- OAI.Combinatorics.EditApproximation.Probability.AdaptiveSeedLaw
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSeedTables
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalSeedSchedule
- OAI.Combinatorics.EditApproximation.Binary.BinaryMemo
- OAI.Combinatorics.EditApproximation.Geometry.CurrentQueryInputs
- OAI.Combinatorics.EditApproximation.Geometry.GroupInputDependence
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalLocalGroupProgram
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalLocalWarmup
- OAI.Combinatorics.EditApproximation.Probability.FiniteSeedFinal
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalCoarseSeedLaw
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalFinalAccuracy
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalConditionalAccuracy
- OAI.Combinatorics.EditApproximation.Geometry.LocalWideStep
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalLocalRefinement
- OAI.Combinatorics.EditApproximation.Refinement.PhysicalLocalRefinementEquality
- OAI.Combinatorics.EditApproximation.Refinement.ComputedCurrentQueryBudget
- OAI.Combinatorics.EditApproximation.AlmostLinear