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Lax307052.Savitch

Savitch's theorem

concepts/Lax307052/Savitch.lean · lax-307052

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    Theorem

    If ss is fully space-constructible and at least logarithmic, every nondeterministic s(n)s(n)-space decider has a deterministic decider using O(s(n)2)O(s(n)^2) space.

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    1import Lax307052.SpaceConstructibility
    2
    3/-!
    4---
    5title: Savitch's theorem
    6type: theorem
    7---
    8If ss is fully space-constructible and at least logarithmic, every
    9nondeterministic s(n)s(n)-space decider has a deterministic decider using
    10O(s(n)2)O(s(n)^2) space.
    11-/
    12
    13namespace Lax307052.Savitch
    14
    15open Lax434930.PolynomialTime Lax434930.SpaceBounds SpaceConstructibility
    16
    17axiom savitch (s : ℕ → ℕ) (hs : Constructible s)
    18 (hlog : ∀ n, logSpace n ≤ s n) (A : Language) :
    19 A ∈ NSPACE s → ∃ c : ℕ, 0 < c ∧ A ∈ DSPACE (fun n => c * (s n) ^ 2)
    20
    21end Lax307052.Savitch
    22
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