Apologies for the delay! Another quiet month in the property testing world, with only one paper (that we found). If we missed any, let us know in the comments!
On Interactive Proofs of Proximity with Proof-Oblivious Queries, by Oded Goldreich, Guy Rothblum, and Tal Skverer (ECCC). Interactive Proofs of Proximity (IPPs) are the “interactive” version of property testers, where the algorithm can both query the input and interact with an all-knowing (but untrusted) prover. In this work, the authors study the power of a specific and natural type of “adaptivity” for IPPs, asking what happens when the choice of queries and the interaction with the prover are independent, or restricted. That is, what happens when these two aspects of the IPP algorithm are in separate “modules”? Can we still test various properties as efficiently? The paper proves various results in under several models (=restrictions between the two “modules”), focusing on the intermediate restriction where the two modules (queries to the input and interaction with the prover) are separate (no interaction), but have access to shared randomness.