Affiliation:
1. University of Memphis, TN
Abstract
The 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 Göös, Pitassi, and Watson (ICALP 2016) is not tight. We also provide a “primal” characterization of this lower bound technique as a complexity class.
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Theory and Mathematics,Theoretical Computer Science
Cited by
2 articles.
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