Lax Lean Archive

Single-tape P is closed under complement

Lax434930.SingleTapeComplement · concepts/Lax434930/SingleTapeComplement.lean · lax-434930

proven

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    Natural Language Statement

    Lemma

    The elementary single-tape class P\mathrm{P} is closed under complement.

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

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    In the paper

    • page 4 of this submission's paper

    Lean source view on GitHub

    1import Lax434930.MachineModels
    2
    3/-!
    4---
    5title: Single-tape P is closed under complement
    6type: lemma
    7---
    8The elementary single-tape class P\mathrm{P} is closed under complement.
    9-/
    10
    11namespace Lax434930.SingleTapeComplement
    12
    13open PolynomialTime MachineModels
    14
    15/-- Complement closure for the elementary single-tape definition. -/
    16axiom closed_under_complement (L : Language) :
    17 L ∈ SingleTapeP → Lᶜ ∈ SingleTapeP
    18
    19end Lax434930.SingleTapeComplement
    20
    Show Proof
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