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Lax434930.NondeterministicLogarithmicSpace

The complexity class NL

concepts/Lax434930/NondeterministicLogarithmicSpace.lean · lax-434930

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    Definition

    A binary language belongs to NL\mathrm{NL} if a nondeterministic Turing machine decides membership using O(log⁡n)O(\log n) work space and a separate read-only input tape. Every branch halts and respects the space bound; membership means that at least one branch accepts. The bound is c⌊log⁡2(n+2)⌋c\lfloor\log_2(n+2)\rfloor for one positive constant cc.

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    1import Lax434930.SpaceBounds
    2
    3/-!
    4---
    5title: The complexity class NL
    6type: definition
    7---
    8A binary language belongs to NL\mathrm{NL} if a nondeterministic Turing
    9machine decides membership using O(log⁡n)O(\log n) work space and a separate
    10read-only input tape. Every branch halts and respects the space bound;
    11membership means that at least one branch accepts. The bound is
    12c⌊log⁡2(n+2)⌋c\lfloor\log_2(n+2)\rfloor for one positive constant cc.
    13-/
    14
    15namespace Lax434930.NondeterministicLogarithmicSpace
    16
    17open PolynomialTime SpaceBounds
    18
    19/-- Nondeterministic logarithmic work space. -/
    20def NL : Set Language :=
    21 {A | ∃ c : ℕ, 0 < c ∧ A ∈ NSPACE (fun n => c * logSpace n)}
    22
    23end Lax434930.NondeterministicLogarithmicSpace
    24

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