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2f887db | 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 | import Mathlib
import OAI.Computability.MinUncut.Machines.UnboundedGraphMachine
namespace OAI
section
namespace MinUncut.Costed.Arena
open _root_.Turing _root_.OAI.Turing _root_.Turing.PartrecToTM2 _root_.OAI.Turing.PartrecToTM2 Turing.ToPartrec Polynomial
open MinUncutGames.Foundations.Complexity
noncomputable section
def unboundedGraphMachine_outputs_base {c : Code} {v : List ℕ} {B n k : ℕ}
{table : List Bool} {rest : List ℕ} (base : Heap)
(hc : Runs c v (n::(table.map Bool.toNat++2::k::rest)) B)
(hl : (n::(table.map Bool.toNat++2::k::rest)).length≤B) :
TM2OutputsInTime unboundedGraphMachine (trList ((initialState c v base).encode))
(some (MinUncutGames.BinaryEncoding.nameBits n++table++MinUncutGames.BinaryEncoding.nameBits k))
(unboundedGraphTime.eval (magnitude (B::(initialState c v base).encode))) := by
apply Classical.choice
obtain ⟨h,hr,hm⟩ := unboundedWords_run hc hl base
let junk := rest++(n::(table.map Bool.toNat++2::k::rest)).reverse++2::words h
have he' : (n::(table.map Bool.toNat++2::k::rest))++
(n::(table.map Bool.toNat++2::k::rest)).reverse++2::words h=
n::(table.map Bool.toNat++2::k::junk) := by
simp only [List.cons_append,List.append_assoc,junk]
rw [he'] at hr hm
obtain ⟨t,ht,hr⟩ := hr
have h1 := hr.finiteMachine
have h2 := GraphCodec.outputsInTime n k table junk
have h2' : TM2OutputsInTime GraphCodec.machine
((trList (n::(table.map Bool.toNat++2::k::junk))).map id)
(some (MinUncutGames.BinaryEncoding.nameBits n++table++MinUncutGames.BinaryEncoding.nameBits k))
(2*bitsize (n::(table.map Bool.toNat++2::k::junk))+
(MinUncutGames.BinaryEncoding.nameBits n++table++MinUncutGames.BinaryEncoding.nameBits k).length+2) := by
have input_eq : @List.map (GraphCodec.machine.Γ GraphCodec.machine.k₀)
(GraphCodec.machine.Γ GraphCodec.machine.k₀) id
(trList (n::(table.map Bool.toNat++2::k::junk))) =
trList (n::(table.map Bool.toNat++2::k::junk)) := List.map_id _
simpa only [input_eq] using h2
have hh := MachineSequential.execute (codeMachine unboundedWordsCode) GraphCodec.machine id Γ'.cons
_ _ _ _ _ h1 h2'
have hb := bitsize_le_magnitude (n::(table.map Bool.toNat++2::k::junk))
have ho := GraphRegisters.codec_length_le n k table junk
refine ⟨⟨hh.toEvalsTo,hh.steps_le_m.trans ?_⟩⟩
change t+1+2*((trList (n::(table.map Bool.toNat++2::k::junk))).length+1)+
(2*bitsize (n::(table.map Bool.toNat++2::k::junk))+
(MinUncutGames.BinaryEncoding.nameBits n++table++MinUncutGames.BinaryEncoding.nameBits k).length+2)≤_
simp only [unboundedGraphTime,eval_add,eval_mul,eval_C,eval_ofNat]
simp only [bitsize] at hb ⊢
omega
end
end MinUncut.Costed.Arena
end
end OAI
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