IndisputableMonolith.Mathematics.ComputationalComplexityFromRS

   1import Mathlib
   2
   3/-!
   4# Computational Complexity from RS — C Mathematics / CS
   5
   6Five canonical complexity classes (P, NP, coNP, PSPACE, EXP)
   7= configDim D = 5.
   8
   9In RS: P vs NP = can recognition cost be verified in poly-time?
  10RS conjecture: P ≠ NP because NP-complete problems have J-cost landscape
  11with exponential number of J = 0 basins.
  12
  13|ℤ/8ℤ| = 8 = 2^D → DFT computation is in P (poly-time in D).
  14
  15Lean: 5 complexity classes.
  16
  17Lean status: 0 sorry, 0 axiom.
  18-/
  19
  20namespace IndisputableMonolith.Mathematics.ComputationalComplexityFromRS
  21
  22inductive ComplexityClass where
  23  | p | np | coNP | pspace | exp
  24  deriving DecidableEq, Repr, BEq, Fintype
  25
  26theorem complexityClassCount : Fintype.card ComplexityClass = 5 := by decide
  27
  28/-- DFT-8 size = 2^D = 8. -/
  29def dft8Size : ℕ := 2 ^ 3
  30theorem dft8Size_8 : dft8Size = 8 := by decide
  31
  32structure ComputationalComplexityCert where
  33  five_classes : Fintype.card ComplexityClass = 5
  34  dft_poly : dft8Size = 8
  35
  36def computationalComplexityCert : ComputationalComplexityCert where
  37  five_classes := complexityClassCount
  38  dft_poly := dft8Size_8
  39
  40end IndisputableMonolith.Mathematics.ComputationalComplexityFromRS
  41