Non-interactive proofs of proximity
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Author(s)
Gur, Tom
Rothblum, Ron
Date Issued
June 2016
Journal
computational complexity
Publisher
Springer-Verlag
Citation
Gur, Tom, and Ron D. Rothblum. “Non-Interactive Proofs of Proximity.” Computational Complexity 27, no. 1 (June 3, 2016): 99–207.
Version
Author's final manuscript
Abstract
We initiate a study of non-interactive proofs of proximity. These proof systems consist of a verifier that wishes to ascertain the validity of a given statement, using a short (sublinear length) explicitly given proof, and a sublinear number of queries to its input. Since the verifier cannot even read the entire input, we only require it to reject inputs that are far from being valid. Thus, the verifier is only assured of the proximity of the statement to a correct one. Such proof systems can be viewed as the NP (or more accurately MA) analogue of property testing.
We explore both the power and limitations of non-interactive proofs of proximity. We show that such proof systems can be exponentially stronger than property testers, but are exponentially weaker than the interactive proofs of proximity studied by Rothblum, Vadhan and Wigderson (STOC 2013). In addition, we show a natural problem that has a full and (almost) tight multiplicative trade-off between the length of the proof and the verifier’s query complexity. On the negative side, we also show that there exist properties for which even a linearly long (non-interactive) proof of proximity cannot significantly reduce the query complexity.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00037-016-0136-9
