We revisit the setting of Interactive Proof Systems for Distribution Testing, introduced by Chiesa and Gur (2018), showing that a simple twist on the task requirements may lead to dramatic improvements, allowing verifiers with constant sample complexity.

We define and investigate the multi-prover and zero-knowledge versions of these interactive proof systems, using as flagship example the task of farness verification — the "dual" version of closeness testing. We hope our results will inspire others to investigate and analyze the power and limitations of multiple provers for distribution verification.

Updating author's name (adding middle name, which was missing in the previous submission).

We revisit the setting of Interactive Proof Systems for Distribution Testing, introduced by Chiesa and Gur (2018), showing that a simple twist on the task requirements may lead to dramatic improvements, allowing verifiers with constant sample complexity.

We define and investigate the multi-prover and zero-knowledge versions of these interactive proof systems, using as flagship example the task of farness verification — the "dual" version of closeness testing. We hope our results will inspire others to investigate and analyze the power and limitations of multiple provers for distribution verification.