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Determine the P-dimension of BPP

Determine the polynomial-time dimension of BPP by establishing the exact value of dim_P(BPP) or proving bounds that resolve whether it is zero or positive.

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Background

The authors introduce counting dimensions that refine analyses between P- and PSPACE-dimensions, proving BPP has SharpP-dimension 0. However, the corresponding P-dimension remains unresolved.

Resolving dim_P(BPP) would clarify how strong polynomial-time martingales can be against BPP and relate to longstanding derandomization questions.

References

For example, we show that $BPP$ has $$-dimension 0 and $BQP$ has $GapP$-dimension 0, whereas the $P$-dimensions of these classes remain open.

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