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Lax434930.PolynomialSpace

The complexity class PSPACE

concepts/Lax434930/PolynomialSpace.lean · lax-434930

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    Definition

    A binary language belongs to PSPACE\mathrm{PSPACE} if one deterministic Turing machine decides membership using at most p(n)p(n) work cells on inputs of length nn, for some polynomial p∈N[X]p\in\mathbb{N}[X]. The input tape is read-only and excluded from work space, and the machine always halts.

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

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