Improve verifier time in doubly-efficient interactive proofs

Determine whether, in doubly-efficient interactive proofs for delegating a time T, space S computation (as in Reingold–Rothblum–Rothblum 2021), the verifier’s running time can be reduced from O(S^2 polylog T) to O(S polylog T).

Background

In discussing deterministic debate, the paper compares its results to doubly-efficient interactive proofs for delegating space-bounded computation. The best-known protocols, due to Reingold, Rothblum, and Rothblum (2021), achieve verifier time O(S2 polylog T) for computations running in time T and space S.

The authors note a known gap in the interactive-proofs literature: whether this verifier-time bound can be improved to O(S polylog T). This improvement would significantly reduce verifier overhead and is highlighted as an explicit open question in the cited survey by Goldreich (2018).

References

It is currently an open question whether this can be improved to $O(S\polylog T)$ \citep{goldreich2018doubly}.

— Scalable AI Safety via Doubly-Efficient Debate  (2311.14125 - Brown-Cohen et al., 2023) in Section: Deterministic debate, paragraph comparing to doubly-efficient interactive proofs (after Theorem thm:debate-space)