Super-bit conjecture and failure of SoI for nKt

Determine whether the super-bit conjecture of Rudich implies the failure of Symmetry of Information for nondeterministic time-bounded Kolmogorov complexity nKt.

Background

The paper explains that the standard cryptographic argument for asymmetry of information does not transfer directly from randomized to nondeterministic descriptions. In particular, even if a conditional nondeterministic description is short, it may not provide an efficient way to find a successful computation path and invert a one-way function.

Against this background, the authors explicitly note that the relationship between the super-bit conjecture and failure of Symmetry of Information for nKt is unresolved.

References

We mention that it is also unclear whether the super-bit conjecture of \citep{DBLP:conf/random/Rudich97} implies the failure of SoI for $nKt$.

— Asymmetry and Complexity of Nondeterministic Computations  (2610.20188 - Goldberg et al., 14 Oct 2026) in Section 1, subsection “Context and Motivation,” footnote

While we are currently unable to determine, unconditionally, if symmetry of information fails in a nondeterministic setting, we obtain an unconditional result in the presence of a conditional string, which one can think of as an advice string or side information.

— Asymmetry and Complexity of Nondeterministic Computations  (2610.20188 - Goldberg et al., 14 Oct 2026) in Section 1, subsection “An Unconditional Failure of SoI via Computational Hardness”