GapP-measure of SPP

Determine whether the class SPP has zero GapP-measure by proving or refuting mu_{GapP}(SPP)=0.

Background

The authors show that GapP-random languages avoid SPP and note that SPP is low for GapP (GapPSPP = GapP). However, a uniform measure-zero result for SPP under GapP-measure is not established.

Proving mu_{GapP}(SPP)=0 would align the lowness and randomness results with a global measure classification of SPP under counting martingales.

References

We do not know if $SPP$ languages can be shown to uniformly have $GapP$-measure 0.

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