Lax Lean Archive

BPP is contained in PP

Lax115662.BPPSubsetPP · concepts/Lax115662/BPPSubsetPP.lean · lax-115662

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.

    Natural Language Statement

    Theorem

    Bounded-error polynomial time is contained in unbounded-error polynomial time: BPP⊆PP\mathrm{BPP}\subseteq\mathrm{PP}. The same procedure witnesses the inclusion, since 2/3>1/22/3>1/2.

    Concept map
    5 concepts
    100%
    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    Each proof establishes this claim relative to its assumptions.

    Lean source view on GitHub

    1import Lax115662.RandomizedPolynomialTime
    2import Lax115662.UnboundedError
    3
    4/-!
    5---
    6title: BPP is contained in PP
    7type: theorem
    8---
    9Bounded-error polynomial time is contained in unbounded-error polynomial
    10time: BPP⊆PP\mathrm{BPP}\subseteq\mathrm{PP}.
    11The same procedure witnesses the inclusion, since 2/3>1/22/3>1/2.
    12-/
    13
    14namespace Lax115662.BPPSubsetPP
    15
    16open RandomizedPolynomialTime UnboundedError
    17
    18axiom BPP_subset_PP : BPP ⊆ PP
    19
    20end Lax115662.BPPSubsetPP
    21
    Show Proof
    Builds on
    Used by

    none

    From Mathlib

    none

    Discussion

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

    Loading discussion…