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Lax307052.SpaceConstructibility

Space-constructible bounds

concepts/Lax307052/SpaceConstructibility.lean · lax-307052

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    Definition

    A positive bound ss is fully space-constructible if a deterministic machine, on each input of length nn, halts at work position s(n)−1s(n)-1 without leaving the first s(n)s(n) work cells. The input tape is read-only.

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    1import Lax434930.SpaceBounds
    2
    3/-!
    4---
    5title: Space-constructible bounds
    6type: definition
    7---
    8A positive bound ss is fully space-constructible if a deterministic
    9machine, on each input of length nn, halts at work position s(n)−1s(n)-1
    10without leaving the first s(n)s(n) work cells. The input tape is read-only.
    11-/
    12
    13namespace Lax307052.SpaceConstructibility
    14
    15open Lax434930.PolynomialTime Lax434930.SpaceMachines
    16
    17def Constructible (s : ℕ → ℕ) : Prop :=
    18 ∃ M : Machine, M.Deterministic ∧ ∀ w : Word,
    19 M.HaltsOn w ∧ M.UsesSpace w (s w.length) ∧
    20 ∃ (t : ℕ) (c : M.Config), M.Run w t c ∧ M.Terminal w c ∧
    21 c.workHead + 1 = s w.length
    22
    23end Lax307052.SpaceConstructibility
    24

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