Separating MnKtP from NP

Prove that the nondeterministic meta-complexity problem MnKtP does not belong to NP.

Background

The paper obtains an unconditional lower bound showing that the randomized problem MrnKtP is not in AM, along with stronger lower bounds for related gap problems. It does not obtain the analogous NP lower bound for MnKtP.

The authors explicitly distinguish this unresolved question from their established results, making it a concrete open problem about the complexity of deciding whether a string has a short nondeterministic Levin-style description.

References

While we were able to establish that $\mathsf{MrnKtP} \notin \mathsf{AM}$, it remains an interesting open problem to show that $\mathsf{MnKtP} \notin NP$.

— Asymmetry and Complexity of Nondeterministic Computations  (2610.20188 - Goldberg et al., 14 Oct 2026) in Section 1, subsection “Lower Bounds for rnKt via Explicit Constructions”