A ZPPNP lifting 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.
Leibniz International Proceedings in Informatics, LIPIcs
Watson, T. (2019). A ZPPNP lifting theorem. Leibniz International Proceedings in Informatics, LIPIcs, 126 https://doi.org/10.4230/LIPIcs.STACS.2019.59