Defining useful randomized debate variants

Develop rigorous formal definitions of randomized debate protocols beyond the specific randomised-verifier model where a decision tree computes the verifier function V with bounded error, ensuring that such variants remain convincing and useful (i.e., retain completeness and soundness properties analogous to the deterministic two-prover, query-bounded verifier setting).

Background

The paper introduces Debate Query Complexity (DQC) in a deterministic two-prover setting with a query-bounded verifier and later considers a specific notion of a randomised verifier as a randomised decision tree computing the verifier function V with bounded error. While lower bounds are established for this model, the authors note uncertainty about how to generalise randomness in debate protocols such that the resulting systems remain compelling and reliable.

This problem seeks principled design and formalisation of other randomized debate variants (e.g., randomness in the verifier or protocol structure) that preserve the essential guarantees of debate—namely that an honest prover can force the correct outcome against any strategy by a dishonest opponent—so that these variants are both theoretically sound and practically useful.