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I'm curious about whether there are any complete problems in the Arthur-Merlin complexity class. Graph Non-Isomorphism (GNI) seems to be the canonical "example" of a problem in AM, but it's never mentioned as a complete one.

I suppose I'm also wondering if a "complete" problem is well-defined for AM. Since AM = BP.NP, it seems the go to "reduction" to AM relies on randomized reductions to 3SAT rather than the Karp reductions we use for deterministic complexity classes. So maybe since Karp reductions have no error, "Karp reducing to an AM problem" doesn't really have any meaning, thus invalidating the usual notion we use of a "complete" problem?

I'm curious about whether there are any complete problems in the Arthur-Merlin complexity class. Graph Non-Isomorphism (GNI) seems to be the canonical example of a problem in AM, but it's probably not a complete one.

I suppose I'm also wondering if a "complete" problem is well-defined for AM. Since AM = BP.NP, it seems the go to "reduction" to AM relies on randomized reductions to 3SAT rather than the Karp reductions we use for deterministic complexity classes. So maybe since Karp reductions have no error, "Karp reducing to an AM problem" doesn't really have any meaning, thus invalidating the usual notion we use of a "complete" problem?