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Lax307052.SearchMachine

Space bound for the search machine

concepts/Lax307052/SearchMachine.lean · lax-307052

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A

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    Lemma

    The deterministic machine constructs the space bound, encodes configurations, and evaluates recursive reachability using parallel stacks. Its work space is quadratic in the original machine's space bound.

    Lean source view on GitHub

    1import Lax307052.ConfigurationGraph
    2import Lax307052.SpaceConstructibility
    3
    4/-!
    5---
    6title: Space bound for the search machine
    7type: lemma
    8---
    9The deterministic machine constructs the space bound, encodes configurations,
    10and evaluates recursive reachability using parallel stacks. Its work space
    11is quadratic in the original machine's space bound.
    12-/
    13
    14namespace Lax307052.SearchMachine
    15
    16open Lax434930.PolynomialTime Lax434930.SpaceMachines Lax434930.SpaceBounds
    17open ConfigurationGraph SpaceConstructibility
    18
    19axiom implement (M : Machine) (s : ℕ → ℕ) (hs : Constructible s)
    20 (hlog : ∀ n, logSpace n ≤ s n)
    21 (hM : ∀ w, M.UsesSpace w (s w.length)) :
    22 ∃ (c : ℕ) (D : Machine), 0 < c ∧ D.Deterministic ∧
    23 (∀ w, D.HaltsOn w ∧ (D.Accepts w ↔ SearchAccepts M w (s w.length))) ∧
    24 ∀ w, D.UsesSpace w (c * (s w.length) ^ 2)
    25
    26end Lax307052.SearchMachine
    27
    Show Proof

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