Lax Lean Archive

ZPP is contained in BPP

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

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

    Zero-error polynomial time is contained in bounded-error polynomial time: ZPP⊆BPP\mathrm{ZPP}\subseteq\mathrm{BPP}. The proof combines the inclusion of ZPP in RP with the inclusion of the one-sided-error classes in BPP.

    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 Lax666725.RandomizedPolynomialTime
    2import Lax666725.ZeroError
    3
    4/-!
    5---
    6title: ZPP is contained in BPP
    7type: theorem
    8---
    9Zero-error polynomial time is contained in bounded-error polynomial time:
    10ZPP⊆BPP\mathrm{ZPP}\subseteq\mathrm{BPP}.
    11The proof combines the inclusion of ZPP in RP with the inclusion of the
    12one-sided-error classes in BPP.
    13-/
    14
    15namespace Lax666725.ZPPSubsetBPP
    16
    17open RandomizedPolynomialTime ZeroError
    18
    19axiom ZPP_subset_BPP : ZPP ⊆ BPP
    20
    21end Lax666725.ZPPSubsetBPP
    22
    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…