Polynomial-time lower bound for MKtP

Prove unconditionally that the meta-complexity problem MKtP is not in P.

Background

MKtP asks whether a string has Levin–Kolmogorov complexity at most a specified threshold. Establishing that this problem is not solvable in polynomial time is a foundational open problem in meta-complexity.

The paper derives stronger lower bounds for related nondeterministic and randomized problems, but explicitly records that the polynomial-time lower bound for MKtP itself remains unresolved.

References

Recall that showing that $MKtP \notin P$ is a longstanding open problem in meta-complexity that dates back at least to \citep{DBLP:journals/siamcomp/AllenderBKMR06}.

— Asymmetry and Complexity of Nondeterministic Computations  (2610.20188 - Goldberg et al., 14 Oct 2026) in Section 1, subsection “Nondeterministic Computation is Likely Asymmetric”