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A ZPP^NP[1] Lifting Theorem

Author Thomas Watson

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LIPIcs.STACS.2019.59.pdf
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Author Details

Thomas Watson
  • University of Memphis, Memphis, TN, USA

Funding

Supported by NSF grant CCF-1657377.

Acknowledgements

I thank Mika Göös and Toniann Pitassi for discussions, and anonymous reviewers for thoughtful comments.

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Thomas Watson. A ZPP^NP[1] Lifting Theorem. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 59:1-59:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.STACS.2019.59

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
Keywords
  • Query complexity
  • communication complexity
  • lifting

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