BPP ⊆ coAM

Inclusion · folklore

Statement

BPP $\subseteq$ coAM — folklore.

Sketch

$\mathbf{BPP}$ is closed under complement, and $\mathbf{BPP}\subseteq \mathbf{AM}$ by the Arthur–Merlin protocol in which Arthur ignores Merlin’s message and runs the BPP decider, so the complement of every BPP language is in $\mathbf{AM}$.