| import OAI.Combinatorics.ContingencyTables.Dense.DenseTrialProgram |
| import OAI.Combinatorics.ContingencyTables.Machines.FirstSuccessProgram |
|
|
| namespace OAI |
|
|
| /-! |
|
|
| 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) |
|
|
| / |
| 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 |
|
|
