P ⊆ BPP

P is contained in BPP.

Statement

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

• $\mathbf{P}\subseteq \mathbf{BPP}\subseteq \mathbf{BQP}$: classical probabilistic computation is a special case of quantum computation.

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.
• Duplicates the corresponding link of the P subset ZPP subset RP subset BPP chain at bounded-error-probabilistic-polynomial-time.md:23 (transitively).
• Purely classical link, so the parent’s model ‘quantum’ does not apply here.