| import Mathlib |
| import OAI.Computability.MinUncut.Machines.FiberGraphMachine |
|
|
| namespace OAI |
|
|
| section |
| noncomputable section |
| namespace MinUncut.Costed.Arena |
| open _root_.Turing _root_.OAI.Turing Turing.ToPartrec _root_.Turing.PartrecToTM2 _root_.OAI.Turing.PartrecToTM2 Polynomial |
| open MinUncutGames.Foundations.Complexity MinUncutGames.BinaryEncoding |
|
|
| def decodedMachine (c : Code) : FinTM2 := |
| MachineSequential.machine FrameDecode.machine (initializedGraphMachine c) id .cons |
| lemma decodedMachine_finite (c : Code) (k : (decodedMachine c).K) : |
| Finite ((decodedMachine c).Γ k) := |
| sequential_finiteAlphabet _ _ _ _ FrameDecode.finiteAlphabet (initializedGraphMachine_finite _) k |
|
|
| def decoded_outputs (c : Code) (K : ℕ) (v out : List Bool) (B : ℕ) |
| (hr : TM2OutputsInTime (initializedGraphMachine c) |
| (trList (K::v.map FrameDecode.symbol)) (some out) B) : |
| TM2OutputsInTime (decodedMachine c) (nameBits K++v) (some out) |
| (B+2*(nameBits K).length+3*(K+1)+4+11*v.length) := by |
| let w:=trList (K::v.map FrameDecode.symbol) |
| let h1:=FrameDecode.outputs K v |
| let h2:TM2OutputsInTime (initializedGraphMachine c) (w.map id) (some out) B:=by |
| have input_eq : @List.map ((initializedGraphMachine c).Γ (initializedGraphMachine c).k₀) |
| ((initializedGraphMachine c).Γ (initializedGraphMachine c).k₀) id w = w := List.map_id _ |
| simpa only [input_eq] using hr |
| have hh:=MachineSequential.execute FrameDecode.machine (initializedGraphMachine c) |
| id Γ'.cons _ _ _ _ _ h1 h2 |
| have hv:=FrameDecode.magnitude_symbols v |
| have hw:w.length≤K+1+3*v.length:=by |
| have h:=(bitsize_le_magnitude (K::v.map FrameDecode.symbol)) |
| simp only [magnitude_cons] at h |
| exact h.trans (by omega) |
| refine ⟨hh.toEvalsTo,hh.steps_le_m.trans ?_⟩ |
| change 2*(nameBits K++v).length+w.length+2+2*(w.length+1)+B≤_ |
| simp only [List.length_append] |
| omega |
| end MinUncut.Costed.Arena |
|
|
| end |
| end |
|
|
| end OAI |
|
|
