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def definition def or abbrev

H_SATTMRuntime

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formal statement (Lean)

 218def H_SATTMRuntime (n m : ℕ) : Prop :=

proof body

Definition body.

 219  ∃ (T : ℕ), T ≤ n * sat_eval_time n m ∧
 220  -- This is the total Turing time for SAT evaluation via CA
 221  IsCorrectTMResult n m T -- SCAFFOLD: IsCorrectTMResult is not yet defined.
 222
 223-- axiom h_sat_tm_runtime : ∀ n m, 0 < n → H_SATTMRuntime n m
 224
 225/-! ## The Key Separation -/
 226
 227/-- **Computation time** for SAT via CA (documentation / TODO): O(n^{1/3} log n)
 228
 229Intended claim: The CA evaluation time for a SAT instance with n variables and m clauses is
 230O(n^{1/3} log(n+m)). This follows from arranging variables in a 3D-like grid on the 1D tape
 231and using parallel propagation. -/
 232/-!

depends on (13)

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