Lax Lean Archive

Correctness of rejection by counting

Lax733996.Rejection · concepts/Lax733996/Rejection.lean · lax-733996

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    Natural Language Statement

    Lemma

    On a space-bounded computation, counting certifies rejection precisely when there is no accepting computation.

    Concept map
    8 concepts
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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

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    In the paper

    • page 2 of this submission's paper

    Lean source view on GitHub

    1import Lax733996.ConfigurationCounting
    2
    3/-!
    4---
    5title: Correctness of rejection by counting
    6type: lemma
    7---
    8On a space-bounded computation, counting certifies rejection precisely when
    9there is no accepting computation.
    10-/
    11
    12namespace Lax733996.Rejection
    13
    14open Lax434930.PolynomialTime Lax434930.SpaceMachines ConfigurationCounting
    15
    16axiom correct (M : Machine) (w : Word) (s : ℕ) (hs : M.UsesSpace w s) :
    17 RejectsByCounting M w s ↔ ¬ M.Accepts w
    18
    19end Lax733996.Rejection
    20
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