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ZPP is contained in RP and coRP

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

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    Natural Language Statement

    Theorem

    Every zero-error polynomial-time language belongs to both one-sided-error classes: ZPP⊆RP∩coRP\mathrm{ZPP}\subseteq\mathrm{RP}\cap\mathrm{coRP}. Replacing "don't know" by rejection gives an RP procedure; replacing it by acceptance gives a coRP procedure.

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
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    Lean source view on GitHub

    1import Lax666725.OneSidedError
    2import Lax666725.ZeroError
    3
    4/-!
    5---
    6title: ZPP is contained in RP and coRP
    7type: theorem
    8---
    9Every zero-error polynomial-time language belongs to both one-sided-error
    10classes: ZPP⊆RP∩coRP\mathrm{ZPP}\subseteq\mathrm{RP}\cap\mathrm{coRP}.
    11Replacing "don't know" by rejection gives an RP procedure; replacing it
    12by acceptance gives a coRP procedure.
    13-/
    14
    15namespace Lax666725.ZPPSubsetOneSided
    16
    17open OneSidedError ZeroError
    18
    19axiom ZPP_subset_RP_inter_coRP : ZPP ⊆ RP ∩ coRP
    20
    21end Lax666725.ZPPSubsetOneSided
    22
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