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d5b7741 | 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 | import OAI.Combinatorics.ContingencyTables.Sampling.ExactPhysicalProgram
import OAI.Combinatorics.ContingencyTables.Sampling.ExactGateTyped
namespace OAI
/-! # The cheap exact-sampling prefix on the same physical program -/
namespace ContingencyTables.ExactGatePhysical
open MatchingFPRAS MatchingFPRAS.PhysicalStream MatchingFPRAS.PhysicalPost
open MatchingFPRAS.TreeTyped MatchingFPRAS.TreePost Turing
open DensePrograms ProfilePrograms
attribute [local irreducible] ExactTypedProgram.program
noncomputable def output (as : List Symbol) (o : Option MatrixCode) :
Cfg Symbol ExactPhysicalProgram.program.State :=
upCfg (OnlineStack.cfg (ExactGateTyped.output as .nil o))
lemma output_some (as : List Symbol) (X : MatrixCode) :
output as (some X)=ExactPhysicalProgram.program.final
(Tape.mk₁ (packed (GreedyFeasibleTable.printMatrix X))) := by
change upCfg (OnlineStack.cfg
(⟨none,none,inputStacks (GreedyFeasibleTable.printMatrix X)⟩ :
OnlineTree.StoreCfg ExactTypedProgram.program))=_
exact OnlineTree.cfg_packed ExactTypedProgram.program (GreedyFeasibleTable.printMatrix X) none
lemma output_none_live (as : List Symbol) : (output as none).state≠none := by
change (some _ : Option ExactPhysicalProgram.program.State)≠none
exact Option.some_ne_none _
noncomputable def typedBudget (as : List Symbol) (B : ℕ) : ℕ :=
exactParsedMarginsRealizer.cost as+ExactGatePrefix.budget (exactParsedMargins as)+B
noncomputable def budget (as : List Symbol) (B : ℕ) : ℕ :=
typedBudget as B*OnlineStack.Executes.factor ExactTypedProgram.program.code
(weight as) (typedBudget as B)
theorem prefix_correct_cost (as : List Symbol) (B : ℕ)
(hB : (ExactGatePrefix.experiment (exactParsedMargins as)).All
(fun o => o.elim 0 GreedyFeasibleTable.printMatrixRealizer.cost≤B)) :
∃ q,Implements ExactPhysicalProgram.program.table (output as)
(ExactPhysicalProgram.program.initial (Tape.mk₁ (packed as))) q ∧
(∀ g : Option MatrixCode → ℚ,
q.mean g=(ExactGatePrefix.experiment (exactParsedMargins as)).mean g) ∧
q.cost≤budget as B := by
obtain ⟨p,hp,hpm,hpc⟩ := ExactGateTyped.prefix_correct_cost as .nil B hB
obtain ⟨q,hq,hqm,hqc⟩ := hp.compile (weight as) (inputStacks_bound as)
have hu := hq.up
have hi := OnlineTree.cfg_packed ExactTypedProgram.program as (some default)
change upCfg (OnlineStack.cfg (OnlineTree.initial ExactTypedProgram.program (encode as) .nil))=
ExactPhysicalProgram.program.initial (Tape.mk₁ (packed as)) at hi
rw [hi] at hu
refine ⟨q,hu,(fun g => (hqm g).trans (hpm g)),?_⟩
exact hqc.trans (Nat.mul_le_mul hpc (OnlineStack.Executes.factor_mono
(weight as) (weight as) p.cost (typedBudget as B) le_rfl hpc))
end ContingencyTables.ExactGatePhysical
end OAI
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