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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.ExactTypedProgram
import OAI.Combinatorics.ContingencyTables.Sampling.PhysicalPartialSequence
namespace OAI
/-! # Physical execution of the parsed and printed exact sampler -/
namespace ContingencyTables.ExactPhysicalProgram
open MatchingFPRAS MatchingFPRAS.PhysicalStream MatchingFPRAS.PhysicalPost
open MatchingFPRAS.TreeTyped MatchingFPRAS.TreePost Turing
open DensePrograms
noncomputable def ofOnline (P : OnlineProc.Proc (TreeMachine.K TreeFunction.Reg)) : Program where
State := OnlineStack.Q (TreeMachine.K TreeFunction.Reg) (fun _ => Bool)
P.Label RegisterProc.Store
table := liftBool (OnlineStack.table P.code P.coin)
states := OnlineStack.states P.code
supported := liftBool_supported _ _
(OnlineStack.table_supported P.code P.coin)
entry := OnlineStack.initialState
entry_mem := OnlineStack.initialState_mem P.code
noncomputable def program : Program := ofOnline ExactTypedProgram.program
attribute [local irreducible] ExactTypedProgram.program
noncomputable def output (as : List Symbol) (o : Option MatrixCode) : Cfg Symbol program.State :=
upCfg (OnlineStack.cfg (ExactTypedProgram.output as .nil o))
lemma output_some (as : List Symbol) (X : MatrixCode) :
output as (some X)=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 program.State)≠none
exact Option.some_ne_none _
/-- Every finite exact-sampling prefix runs on one fixed finite physical
transition table, including its live failure endpoint. -/
theorem prefix_correct (as : List Symbol) (N : ℕ) :
∃ q,Implements program.table (output as)
(program.initial (Tape.mk₁ (packed as))) q ∧
∀ g : Option MatrixCode → ℚ,
q.mean g=(ExactCoreProgram.prefixExperiment (ProfilePrograms.exactParsedMargins as) N).mean g := by
obtain ⟨p,hp,hpm⟩ := ExactTypedProgram.prefix_correct as .nil N
obtain ⟨q,hq,hqm,_⟩ := 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))=
program.initial (Tape.mk₁ (packed as)) at hi
rw [hi] at hu
exact ⟨q,hu,fun g => (hqm g).trans (hpm g)⟩
end ContingencyTables.ExactPhysicalProgram
end OAI
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