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A ZPPNP[1] Lifting Theorem

Published:08 November 2020Publication History
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Abstract

The complexity class ZPPNP[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: ZPPNP[1] equals the restriction of BPPNP[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 ZPPNP[1] decision tree lower bound for a function f into a ZPPNP[1] communication lower bound for a two-party version of f.

• As an application, we use the above lifting theorem to prove that the ZPPNP[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.

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      • Published in

        cover image ACM Transactions on Computation Theory
        ACM Transactions on Computation Theory  Volume 12, Issue 4
        December 2020
        156 pages
        ISSN:1942-3454
        EISSN:1942-3462
        DOI:10.1145/3427631
        Issue’s Table of Contents

        Copyright © 2020 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 8 November 2020
        • Accepted: 1 August 2020
        • Revised: 1 July 2020
        • Received: 1 December 2018
        Published in toct Volume 12, Issue 4

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