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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 | import OAI.Computability.PerfectCompleteness.Machines.BinaryRenameMachine
import OAI.Computability.PerfectCompleteness.Machines.BinaryTotalInputMachine
import OAI.Computability.UniqueGames.Machines.MachineLemmas
namespace OAI
section
namespace PerfectCompleteness.BinaryInputReduction
open Turing UniqueGamesTheorem.Foundations.Complexity
noncomputable def computation :
TM2ComputableInPolyTime (id : List Bool → List Bool) formulaBits BinaryLanguage.totalRename := by
change TM2ComputableInPolyTime (id : List Bool → List Bool) formulaBits
(fun input => BinaryOccurrenceRename.renamed (BinaryLanguage.totalParsed input))
exact MachineSequential.composeBits BinaryTotalInputMachine.computableInPolyTime
BinaryRenameMachine.computableInPolyTime
theorem computation_finiteAlphabet : MachineFiniteAlphabet.FiniteAlphabet computation.tm :=
MachineFiniteAlphabet.composeBits BinaryTotalInputMachine.computableInPolyTime
BinaryRenameMachine.computableInPolyTime
BinaryTotalInputMachine.computation_finiteAlphabet
BinaryRenameMachine.computation_finiteAlphabet
noncomputable def reduction : CookLevin.PolynomialThreeSATReduction BinaryLanguage.language where
reduce := BinaryLanguage.totalRename
computation := computation
correct input := (BinaryLanguage.totalRename_satisfiable_iff input).symm
theorem reduction_finiteAlphabet : MachineFiniteAlphabet.FiniteAlphabet reduction.computation.tm :=
computation_finiteAlphabet
end PerfectCompleteness.BinaryInputReduction
end
end OAI
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