| import Mathlib |
| import OAI.Computability.MaxCut.Machines.Printer |
| import OAI.Computability.MaxCut.Estimates.Anchor |
|
|
| namespace OAI |
|
|
| noncomputable section |
| namespace OptimalMaxCut.LongCode.InstanceAdapter |
| open scoped BigOperators |
| open MaxCutGames.Foundations.Target CounterMachine Turing |
| attribute [local instance] Classical.propDecidable |
|
|
| theorem exists_gridComputer (q : ℕ) (t : ℚ) (ht : t ∈ Set.Icc (-1:ℚ) 1) (K : ℕ) : |
| ∃ pc : TM2ComputableInPolyTime (bits : Instance q → List Bool) ScaledGraph.bits |
| (fun g => gridGraph g t ht K), ∀ k, Finite (pc.tm.Γ k) := by |
| obtain ⟨len,hlen⟩ := RawGrid.Rep.length q (K+1) |
| obtain ⟨bit,hbit⟩ := RawGrid.Rep.entry q t ht K (K+1) (Expr.Represented.arg 0) |
| have htable (g : Instance q) : table len bit (bits g) = (gridGraph g t ht K).bits := by |
| apply List.ext_getElem |
| · simp only [table,List.length_ofFn,hlen,RawGrid.bits_length] |
| · intro i hi hj |
| have hi' : i<RawGrid.length q (K+1) (bits g) := by |
| simpa only [RawGrid.bits_length] using hj |
| have hh := RawGrid.bits_getD g t ht K i hi' |
| rw [List.getElem?_eq_getElem hj] at hh |
| simp only [Option.getD_some] at hh |
| simp only [table,List.getElem_ofFn,hbit] |
| exact hh.symm |
| let first := tableComputer len bit |
| let pc : TM2ComputableInPolyTime (bits : Instance q → List Bool) ScaledGraph.bits |
| (fun g => gridGraph g t ht K) := { |
| tm := first.tm |
| inputAlphabet := first.inputAlphabet |
| outputAlphabet := first.outputAlphabet |
| time := first.time |
| outputsFun := fun g => by |
| have hh := first.outputsFun (bits g) |
| change TM2OutputsInTime first.tm ((bits g).map first.inputAlphabet.symm) |
| (some ((table len bit (bits g)).map first.outputAlphabet.symm)) _ at hh |
| rw [htable] at hh |
| exact hh } |
| exact ⟨pc, tableComputer_finiteAlphabet len bit⟩ |
|
|
| end OptimalMaxCut.LongCode.InstanceAdapter |
|
|
| end |
|
|
| end OAI |
|
|
