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Worst-case running time of the construction program

Lax235315.ConstructionRuntime · concepts/Lax235315/ConstructionRuntime.lean · lax-235315

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    Natural Language Statement

    Theorem

    For all sufficiently large resource constants K, every run of the fixed construction program on an admissible graph input halts within K(|x|+1)(ceil(log₂ n)+1) steps, including unsuccessful random tapes.

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    Lean source view on GitHub

    1import Lax235315.ConstructionContracts
    2
    3/-!
    4---
    5title: Worst-case running time of the construction program
    6type: theorem
    7---
    8For all sufficiently large resource constants K, every run of the fixed
    9construction program on an admissible graph input halts within
    10K(|x|+1)(ceil(log₂ n)+1) steps, including unsuccessful random tapes.
    11
    12# Formalization notes
    13
    14This is an open implementation obligation for the explicit program.
    15It includes input reading, finite-bit sampling, the guarded arithmetic,
    16partition refinement, near-twin checking and reconstruction. Source-level
    17cost estimates alone do not discharge the registered word-RAM step bound.
    18-/
    19
    20namespace Lax235315.ConstructionRuntime
    21open Lax235315.ConstructionContracts
    22
    23/-- A constant suffices for the time bound on every admissible run. -/
    24axiom eventually_hasRunningTimeBound :
    25 ∃ K₀ : ℕ, 1 ≤ K₀ ∧ ∀ K : ℕ, K₀ ≤ K → HasRunningTimeBound K
    26
    27end Lax235315.ConstructionRuntime
    28
    Formalization notes

    This is an open implementation obligation for the explicit program. It includes input reading, finite-bit sampling, the guarded arithmetic, partition refinement, near-twin checking and reconstruction. Source-level cost estimates alone do not discharge the registered word-RAM step bound.

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