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Determine the P-measures of NP and UP

Determine the polynomial-time resource-bounded measures of NP and UP by establishing whether mu_P(NP)=0 and mu_P(UP)=0, respectively, or proving they are nonzero.

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Background

It is known that NP and UP have PSPACE-measure 0, but their P-measures remain unresolved. The paper introduces intermediate counting-measure notions that sometimes bridge the gap between P and PSPACE, yet they do not settle the P-measures of NP and UP.

Resolving these measures would have far-reaching implications, given prior connections between measure hypotheses and complexity class separations.

References

We also know that $NP$ and $UP$ have $PSPACE$-measure 0, but we do not know their $P$-measures.

— Counting Martingales for Measure and Dimension in Complexity Classes (2508.07619 - Hitchcock et al., 11 Aug 2025) in Section 7, Conclusion