AM = coAM

AM is equal to coAM.

Statement

Migrated verbatim from co-arthur-merlin § Co-Arthur-Merlin:

The complement class of AM: a problem is in coAM if its complement is in AM. Equivalently, coAM is the class of problems for which a “no” answer has an Arthur-Merlin protocol — Arthur sends a random challenge, Merlin responds, and Arthur can verify “no” answers with high probability.

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:

  • Definitional (complementation), not a theorem; the migration probably wants a distinct ‘complement-of’ edge type.