The class of functions computable in randomized polynomial time with a shared, untrusted witness for each input size. The input-oblivious version of MA.
L is in OMA if there exists a randomized, polynomial time verifier V taking an input and a witness, so that:
NP is contained in OMA iff NP is in P/poly [FSW09].
EXP is contained in P/poly iff EXP = OMA [FSW09].
BPP is contained in OMA [GM15].
Implicit in [San07] that OMA/1 (that is, OMA with 1 bit of trusted advice) does not have circuits of size for any .
The class of decision problems solvable by a Merlin-Arthur protocol, which goes as follows. Merlin, who has unbounded computational resources, sends Arthur a polynomial-size purported proof that the answer to the problem is "yes." Arthur must verify the proof in BPP (i.e. probabilistic polynomial-time), so that
Defined in [Bab85].
An alternative definition requires that if the answer is "yes," then there exists a proof such that Arthur accepts with certainty. However, the definitions with one-sided and two-sided error can be shown to be equivalent (see [FGM+89]).
Contains NP and BPP (in fact also ∃BPP), and is contained in AM and in QMA.
There exists an oracle relative to which BQP is not in MA [Wat00].
Equals NP under a derandomization assumption: if E requires exponentially-sized circuits, then PromiseBPP = PromiseP, implying that MA = NP [IW97].
Shown in [San07] that MA/1 (that is, MA with 1 bit of advice) does not have circuits of size for any . In the same paper, the result was used to show that MA/1 cannot be solved on more than a fraction of inputs having length by any circuit of size . Finally, it was shown that MA does not have arithmetic circuits of size .