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Lax434930.LogarithmicSpace

The complexity class L

concepts/Lax434930/LogarithmicSpace.lean · lax-434930

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    Definition

    A binary language belongs to L\mathrm{L} if a deterministic Turing machine decides membership using O(log⁡n)O(\log n) work space and a separate read-only input tape. Precisely, some positive constant cc bounds work space by c⌊log⁡2(n+2)⌋c\lfloor\log_2(n+2)\rfloor on every input of length nn.

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    1import Lax434930.SpaceBounds
    2
    3/-!
    4---
    5title: The complexity class L
    6type: definition
    7---
    8A binary language belongs to L\mathrm{L} if a deterministic Turing machine
    9decides membership using O(log⁡n)O(\log n) work space and a separate read-only
    10input tape. Precisely, some positive constant cc bounds work space by
    11c⌊log⁡2(n+2)⌋c\lfloor\log_2(n+2)\rfloor on every input of length nn.
    12-/
    13
    14namespace Lax434930.LogarithmicSpace
    15
    16open PolynomialTime SpaceBounds
    17
    18/-- Deterministic logarithmic work space. -/
    19def L : Set Language :=
    20 {A | ∃ c : ℕ, 0 < c ∧ A ∈ DSPACE (fun n => c * logSpace n)}
    21
    22end Lax434930.LogarithmicSpace
    23

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