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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 | 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
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