Lax Lean Archive

Draft — mutable and not usable as a dependency; its citation marks the draft state.

Lax554803.SingleTapeComplement

Single-tape P is closed under complement

concepts/Lax554803/SingleTapeComplement.lean · lax-554803

proven

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.

    Concept map

    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A

    Evidence

    Each proof establishes this claim relative to its assumptions.

    Theorem

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

    Lean source view on GitHub

    1import Lax554803.MachineModels
    2
    3/-!
    4---
    5title: Single-tape P is closed under complement
    6type: theorem
    7---
    8The elementary single-tape class P\mathrm{P} is closed under complement.
    9-/
    10
    11namespace Lax554803.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 Lax554803.SingleTapeComplement
    20
    Show Proof

    Builds on

    Used by

    none

    From Mathlib

    none

    Community review

    Discussion

    Ask a question or add context. Endorsements and structured flags are kept in the review panel above; your ORCID profile must share a public name.

    0 comments

    Loading discussion…