ECCC-Report TR17-139https://eccc.weizmann.ac.il/report/2017/139Comments and Revisions published for TR17-139en-usMon, 18 Sep 2017 23:32:16 +0300
Paper TR17-139
| A ZPP^NP[1] Lifting Theorem |
Thomas Watson
https://eccc.weizmann.ac.il/report/2017/139The complexity class ZPP^NP[1] (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: ZPP^NP[1] equals the restriction of BPP^NP[1] 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 ZPP^NP[1] decision tree lower bound for a function f into a ZPP^NP[1] communication lower bound for a two-party version of f.
As an application, we use the above lifting theorem to prove that the ZPP^NP[1] communication lower bound technique introduced by Goos, Pitassi, and Watson (ICALP 2016) is not tight. We also provide a "primal" characterization of this lower bound technique as a complexity class.Mon, 18 Sep 2017 23:32:16 +0300https://eccc.weizmann.ac.il/report/2017/139