No need to thank me for my turnabout — we’ve got work to do. There’s a new complexity class in town, and I need you to help me name it.
My new class is like P/poly, except that the polynomial-size advice can’t be trusted — you have to verify it. Or to put it another way, it’s like NP intersect coNP, except that there’s only one witness for each input length. Give me that witness, and I’ll correctly decide every input of size n. Give me a different witness, and for every input of size n I’ll either output the right answer or else say “I don’t know.”
Now, anyone could make up a name for this animal — even I could! But I want the name to be naturally extensible to further classes. For example, if (hypothetically speaking) I was able to use a new result about the learnability of quantum states to prove that AvgBQP/qpoly is contained in AvgQMA/poly, but my proof actually yielded the stronger result that AvgBQP/qpoly is contained in the subclass of AvgQMA/poly where there’s only one QMA witness for each input length, then your naming convention should immediately give me a name for that subclass.
So let the christening commence! And for extra credit, prove or (relative to an oracle) disprove that if my class contains NP, then P=NP.