Round complexity in PAC-verification

Determine whether there exists a hypothesis class for which any doubly efficient PAC-verification protocol requires more than two rounds of interaction, and establish whether a hierarchy in round complexity exists for such PAC-verification protocols.

Background

The protocols in the paper are low-round and doubly efficient. Understanding the minimal number of rounds needed for various hypothesis classes could reveal inherent interaction complexity in verification tasks and inform protocol design.

A round hierarchy—analogous to those in interactive proofs—would indicate strictly increasing power with more rounds for learning verification, a fundamental structural insight.