coNP ⊆ AM

coNP is contained in AM.

Statement

Migrated verbatim from co-nondeterministic-polynomial-time § Known relationships:

• $\mathbf{coNP}\subseteq \mathbf{AM}$: this follows from the result of GS86 showing that coNP has Arthur-Merlin protocols.

Notes

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:

• SUSPECTED MATHEMATICAL ERROR (report only): coNP contained in AM is NOT known — it would collapse the polynomial hierarchy to AM (in particular to the second level). GS86 proves the private-coin/public-coin equivalence, not that coNP has AM protocols.
• The claim also contradicts content/Complexity/co-arthur-merlin.md:21, whose collapse argument presumes coNP is NOT known to be in AM, and content/Complexity/co-arthur-merlin.md:20, which only claims coNP in coAM.
• Citation is attached to a statement the cited paper does not make.