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BPP is contained in PP

Lax666725.BPPSubsetPP · concepts/Lax666725/BPPSubsetPP.lean · lax-666725

proven

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    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.

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    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 Lax666725.RandomizedPolynomialTime
    2import Lax666725.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 Lax666725.BPPSubsetPP
    15
    16open RandomizedPolynomialTime UnboundedError
    17
    18axiom BPP_subset_PP : BPP ⊆ PP
    19
    20end Lax666725.BPPSubsetPP
    21
    Show Proof
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