Approximate counting for GapP

Determine whether GapP functions admit efficient approximate counting analogous to known approximations for SpanP (and #P), for example by developing deterministic algorithms with appropriate oracle access that approximate GapP functions within specified relative error.

Background

The paper uses approximate counting for SpanP to convert SpanP-martingales to weaker-resource supermartingales, enabling measure conservation within E with low-level oracles. Such approximations are known for #P and SpanP via Stockmeyer and derandomization results.

An analogous approximation for GapP would extend these conservation results and strengthen the toolkit for measuring quantum-related classes, but whether this is possible remains unknown.