A ZPPNPlifting theorem
The complexity class ZPPNP (corresponding to zero-error randomized algorithms with access to one NP oracle query) is known to have a number of curious properties. We further explore this class in the settings of time complexity, query complexity, and communication complexity. • For starters, we provide a new characterization: ZPPNP equals the restriction of BPPNP where the algorithm is only allowed to err when it forgoes the opportunity to make an NP oracle query. • Using the above characterization, we prove a query-to-communication lifting theorem, which translates any ZPPNP decision tree lower bound for a function f into a ZPPNP communication lower bound for a two-party version of f. • As an application, we use the above lifting theorem to prove that the ZPPNP communication lower bound technique introduced by Göös, Pitassi, and Watson (ICALP 2016) is not tight. We also provide a "primal"characterization of this lower bound technique as a complexity class.
ACM Transactions on Computation Theory
Watson, T. (2020). A ZPPNPlifting theorem. ACM Transactions on Computation Theory, 12 (4) https://doi.org/10.1145/3428673