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RP and coRP are contained in BPP

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

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    Natural Language Statement

    Theorem

    The one-sided-error classes satisfy RP∪coRP⊆BPP\mathrm{RP}\cup\mathrm{coRP}\subseteq\mathrm{BPP}. Their one-sided guarantees imply correctness with probability at least 2/32/3 on every input.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

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    Lean source view on GitHub

    1import Lax666725.RandomizedPolynomialTime
    2import Lax666725.OneSidedError
    3
    4/-!
    5---
    6title: RP and coRP are contained in BPP
    7type: theorem
    8---
    9The one-sided-error classes satisfy
    10RP∪coRP⊆BPP\mathrm{RP}\cup\mathrm{coRP}\subseteq\mathrm{BPP}.
    11Their one-sided guarantees imply correctness with probability at least
    122/32/3 on every input.
    13-/
    14
    15namespace Lax666725.OneSidedSubsetBPP
    16
    17open RandomizedPolynomialTime OneSidedError
    18
    19axiom RP_union_coRP_subset_BPP : RP ∪ coRP ⊆ BPP
    20
    21end Lax666725.OneSidedSubsetBPP
    22
    Show Proof
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