RecognitionComplete

formal source

  53namespace ComputationBridge
  54
  55/-- Recognition-complete complexity: dual complexity parameters (Tc, Tr) -/
  56structure RecognitionComplete where
  57  /-- Computation complexity: internal evolution steps -/
  58  Tc : ℕ → ℕ
  59  /-- Recognition complexity: observation operations -/
  60  Tr : ℕ → ℕ
  61  /-- Computation is sub-polynomial -/
  62  Tc_subpoly : ∃ (c : ℝ) (k : ℝ), 0 < k ∧ k < 1 ∧ ∀ n, n > 0 → Tc n ≤ c * n^k * Real.log n
  63  /-- Recognition is at least linear -/
  64  Tr_linear : ∃ (c : ℝ), c > 0 ∧ ∀ n, n > 0 → Tr n ≥ c * n
  65
  66/-- The Turing model as a special case with zero recognition complexity. -/
  67structure TuringModel where
  68  /-- Turing time complexity -/
  69  T : ℕ → ℕ
  70  /-- Recognition complexity is zero in the Turing model. -/
  71  recognition_complexity : ℕ → ℕ
  72  recognition_free : ∀ n, recognition_complexity n = 0
  73
  74/-- Ledger-based computational model with explicit observation cost -/
  75
  76structure LedgerComputation where
  77  /-- State space (ledger configurations) -/
  78  states : Type
  79  /-- Evolution rule (double-entry updates) -/
  80  evolve : states → states
  81  /-- Input encoding into ledger -/
  82  encode : List Bool → states
  83  /-- Output protocol (measurement operations) -/
  84  measure : states → Finset (Fin n) → Bool
  85  /-- Evolution preserves closed-chain flux = 0 -/
  86  flux_conserved : ∀ s, evolve s = s  -- placeholder for actual conservation