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Lax434930.NondeterministicPolynomialSpace

The complexity class NPSPACE

concepts/Lax434930/NondeterministicPolynomialSpace.lean · lax-434930

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    Definition

    A binary language belongs to NPSPACE\mathrm{NPSPACE} if one nondeterministic Turing machine decides membership using at most p(n)p(n) work cells on every branch on inputs of length nn, for some polynomial p∈N[X]p\in\mathbb{N}[X]. All branches halt; at least one accepts precisely when the input belongs to the language. The input tape is read-only and excluded from work space.

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    1import Lax434930.SpaceBounds
    2
    3/-!
    4---
    5title: The complexity class NPSPACE
    6type: definition
    7---
    8A binary language belongs to NPSPACE\mathrm{NPSPACE} if one nondeterministic
    9Turing machine decides membership using at most p(n)p(n) work cells on
    10every branch on inputs of length nn, for some polynomial
    11p∈N[X]p\in\mathbb{N}[X]. All branches halt; at least one accepts precisely
    12when the input belongs to the language. The input tape is read-only and
    13excluded from work space.
    14-/
    15
    16namespace Lax434930.NondeterministicPolynomialSpace
    17
    18open PolynomialTime SpaceBounds
    19
    20/-- Nondeterministic polynomial work space. -/
    21def NPSPACE : Set Language :=
    22 {A | ∃ p : Polynomial ℕ, A ∈ NSPACE p.eval}
    23
    24end Lax434930.NondeterministicPolynomialSpace
    25

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