coNP ⊆ coAM

coNP is contained in coAM.

Statement

Migrated verbatim from co-arthur-merlin § Known relationships:

• $\mathbf{coNP}\subseteq \mathbf{coAM}$, since $\mathbf{NP}\subseteq \mathbf{AM}$ (by GS86) and taking complements.

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 SUB-EDGE WHILE THE PARENT IS CITED: GS86 sits on the parent but is attached to the NP-in-AM half only.
• CONTRADICTION ACROSS PAGES (recorded, not fixed): co-nondeterministic-polynomial-time.md:20 asserts coNP subset AM, which would collapse the polynomial hierarchy; only one of the two pages can be right.
• ‘taking complements’ is a meta-derivation step rather than a reduction, and has no representation in the model.