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ea76aac | 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 | 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
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