Is there any example of any natural problem which is known to be in MA, but not yet to known to be in NP?

I am aware that Graph Nonisomorphism (GNI) is known to be in AM which is considered a superset of MA. Can we construct a language (which may be non-natural) which is in MA, but not in NP?

  • $\begingroup$ Since MA is in the polynomial hierarchy, there is no such unconditional result. $\endgroup$ Nov 24, 2017 at 16:06

1 Answer 1


The same hardness assumption that implies P=BPP also implies NP=MA (at least according to the complexity zoo).

Even if the hardness assumption is wrong, separating NP from MA would be a huge achievement, since it would imply that P is different from NP (as MA is in the polynomial hierarchy).

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    $\begingroup$ Yes. separating NP from MA unconditionally would be very hard. (even showing their equality will lead to NEXP $\not\subset$ P/poly, which seems very hard to prove). But my question is a little different: Is something known to be in MA, but not (known) to be in NP (or at least we are unable to prove it is in NP yet)? For example: We can prove GNI is in AM, but it is not known to be in MA (or NP) yet. (Still they are not ruled out). $\endgroup$ Nov 24, 2017 at 16:46
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    $\begingroup$ For example: A lot of problems are known to be in BPP, but not in P (Polynomial Identity Testing being one example). Similarly, Does the same thing happen in their non-deterministic counterpart as well? $\endgroup$ Nov 24, 2017 at 16:52

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