Lax Lean Archive

PSPACE-completeness

Lax689614.PSPACE · concepts/Lax689614/PSPACE.lean · lax-689614

definition

Loading review…

Community review

Flags

Each flag is tied to a public ORCID identity and explains why this concept may be incorrect.

No flags have been submitted.

    Community review

    Flag this concept

    State precisely what appears incorrect. This explanation will be public under your ORCID name.

    No source line selected.

    Natural Language Statement

    Definition

    A binary language is PSPACE-hard if every language decidable in polynomial space has a polynomial-time many-one reduction to it. It is PSPACE-complete if it is also decidable in polynomial space. Polynomial space and reductions are those of the classical complexity and Cook–Levin submissions.

    Concept map
    8 concepts; 3 descendants hidden
    100%
    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A

    Lean source view on GitHub

    1import Lax434930.PolynomialSpace
    2import Lax429075.Reductions
    3
    4/-!
    5---
    6title: PSPACE-completeness
    7type: definition
    8---
    9A binary language is PSPACE-hard if every language decidable in polynomial
    10space has a polynomial-time many-one reduction to it. It is PSPACE-complete
    11if it is also decidable in polynomial space. Polynomial space and reductions
    12are those of the classical complexity and Cook–Levin submissions.
    13-/
    14
    15namespace Lax689614.PSPACE
    16
    17open Lax434930.PolynomialTime Lax434930.PolynomialSpace Lax429075.Reductions
    18
    19def Hard (B : Language) : Prop := ∀ A : Language, A ∈ PSPACE → ManyOne A B
    20
    21def Complete (B : Language) : Prop := B ∈ PSPACE ∧ Hard B
    22
    23end Lax689614.PSPACE
    24
    Builds on
    Used by
    From Mathlib

    none

    Discussion

    Ask a question or add context. Endorsements and structured flags are kept in the review panel above.

    Loading discussion…