ZPP ⊆ RP

ZPP is contained in RP.

Statement

Migrated verbatim from bounded-error-probabilistic-polynomial-time § Known relationships:

• $\mathbf{P}\subseteq \mathbf{ZPP}\subseteq \mathbf{RP}\subseteq \mathbf{BPP}$: deterministic algorithms are a special case of Las Vegas, which are a special case of one-sided error, which are a special case of two-sided error.

Migrated verbatim from zero-error-probabilistic-polynomial-time § Known relationships:

• $\mathbf{P}\subseteq \mathbf{ZPP}\subseteq \mathbf{RP}\subseteq \mathbf{BPP}$.

Notes

source: folklore: the claim carried no citation on the page it was migrated from, and none was invented.

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

class: free because a containment between complexity classes is proved by any argument at all; the reduction-class axis does not discriminate here, and unstated would wrongly suggest the information is missing.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• Uncited and unlabelled folklore.
• randomized-polynomial-time exists as a page but appears only as the \classRP macro, with no wikilink.
• Uncited and unjustified.
• Follows immediately from the page’s own ZPP = RP intersect coRP identity at line 15, which the bullet does not connect.