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97c3405 | 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 | import OAI.Combinatorics.ContingencyTables.Dense.DenseTrialProgram
import OAI.Combinatorics.ContingencyTables.Machines.FirstSuccessProgram
namespace OAI
/-! # The bounded dense draw as a single polynomial binary program -/
namespace ContingencyTables.DensePrograms
open MatchingFPRAS.TreeTyped ProfilePrograms
abbrev DenseDrawParameters := FlatExponentData×ℕ
abbrev DenseDrawData := (DenseDrawParameters×MatrixCode)×List Bool
def trialWidth (z : DenseDrawParameters) : ℕ :=
trialWalkBits (z,[])+(offsetLengths (flatToGridData z.1,z.2)).sum
def trialWidthRealizer : Realizer trialWidth := by
let blank : Realizer (fun z : DenseDrawParameters => (z,([] : List Bool))) :=
pair identity (constant [])
let widths := composition (pair (composition first flatToGridDataRealizer) second)
offsetLengthsRealizer
exact composition (pair (composition blank trialWalkBitsRealizer)
(composition widths listSum)) add
theorem polynomial_trialWidth : PolynomialTime trialWidthRealizer := by
unfold trialWidthRealizer
exact polynomial_composition (polynomial_pair
(polynomial_composition (polynomial_pair polynomial_identity (polynomial_constant []))
polynomial_trialWalkBits)
(polynomial_composition (polynomial_composition (polynomial_pair
(polynomial_composition polynomial_first polynomial_flatToGridData) polynomial_second)
polynomial_offsetLengths) polynomial_listSum)) polynomial_add
def drawChunks (z : DenseDrawData) : List (List Bool) :=
wordChunks (trialWidth z.1.1,z.2)
def drawChunksRealizer : Realizer drawChunks :=
composition (pair (composition (composition first first) trialWidthRealizer) second)
wordChunksRealizer
theorem polynomial_drawChunks : PolynomialTime drawChunksRealizer :=
polynomial_composition (polynomial_pair
(polynomial_composition (polynomial_composition polynomial_first polynomial_first)
polynomial_trialWidth) polynomial_second) polynomial_wordChunks
def denseDrawCode (z : DenseDrawData) : MatrixCode :=
FirstSuccessProgram.retry denseTrialCode (z.1,drawChunks z)
def denseDrawCodeRealizer : Realizer denseDrawCode :=
composition (pair first drawChunksRealizer) (FirstSuccessProgram.retryRealizer denseTrialCodeRealizer)
/-- Every finite input has polynomial binary cost. On a valid dense input,
the first successful trial is selected, or the supplied feasible fallback. -/
theorem polynomial_denseDrawCode : PolynomialTime denseDrawCodeRealizer :=
polynomial_composition (polynomial_pair polynomial_first polynomial_drawChunks)
(FirstSuccessProgram.polynomial_retry polynomial_denseTrialCode)
end ContingencyTables.DensePrograms
end OAI
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