OAI/Combinatorics/ParityLifts/UniformNormalization.lean

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1 declarations, 0 contain sorry, 0 declared as axioms

  1. theorem OAI.ParityWL.Complexity.uniform_eth_unrestricted_exponents line 9

    Source documentation

    Nonnegative exponents and positive multipliers in UniformWLBound are a normalization, not an added restriction on uniform exclusion.

    theorem uniform_eth_unrestricted_exponents (hETH : UniformSubexponentialETH)
        (c : Convention) (i : Implementation) :
        ¬ ∃ (M : Machine) (f g : ℕ → ℝ),
          Filter.Tendsto (fun k : ℕ => g k/k) Filter.atTop (nhds 0) ∧
          ∀ k : ℕ, 4 ≤ k → ∀ (n : ℕ) (G H : SimpleGraph (Fin n)), ∃ s b,
            Emits M (encodeNat k++encodeGraphs G H) s b ∧
            (b=true↔Equivalent G H c i k) ∧ (s : ℝ) ≤ f k*(n+1 : ℝ)^g k := by
    …

    Mentions: OAI.ParityWL.Complexity.UniformSubexponentialETH, OAI.ParityWL.Convention, OAI.ParityWL.Complexity.Implementation, OAI.ParityWL.Complexity.Machine, OAI.ParityWL.Complexity.Emits, OAI.ParityWL.Complexity.encodeNat, OAI.ParityWL.Complexity.encodeGraphs, OAI.ParityWL.Complexity.Equivalent