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Lax307052.FiniteSearch

Deciding finite reachability

concepts/Lax307052/FiniteSearch.lean · lax-307052

proven

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    Lemma

    Recursion depth ⌈log⁡2N⌉\lceil\log_2 N\rceil suffices to decide reachability in a graph with NN vertices.

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    1import Lax307052.Recursion
    2import Lax307052.ShortPaths
    3import Mathlib.Data.Nat.Log
    4
    5/-!
    6---
    7title: Deciding finite reachability
    8type: lemma
    9---
    10Recursion depth ⌈log⁡2N⌉\lceil\log_2 N\rceil suffices to decide reachability
    11in a graph with NN vertices.
    12-/
    13
    14namespace Lax307052.FiniteSearch
    15
    16open Reachability
    17
    18axiom decides_reachability {N : ℕ} (G : Graph N) (a b : Fin N) :
    19 search G (Nat.clog 2 N) a b = true ↔ Reachable G a b
    20
    21end Lax307052.FiniteSearch
    22
    Show Proof

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