New Lower Bounds for Adaptive Tolerant Junta Testing

We prove a k^{-\Omega\left(\log \left(\varepsilon_{2}-\varepsilon_{1}\right)\right)} lower bound for adap- tively testing whether a Boolean function is \varepsilon_{1}-close to or \varepsilon_{2}- far from k-juntas. Our results provide the first superpolynomial separation between tolerant and non-to...

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Bibliographic Details
Published in:Proceedings / annual Symposium on Foundations of Computer Science pp. 1778 - 1786
Main Authors: Chen, Xi, Patel, Shyamal
Format: Conference Proceeding
Language:English
Published: IEEE 06.11.2023
Subjects:
Boolean functions
Computer science
Juntas
Property Testing
Sublinear Algorithms
Testing
Tolerant Testing
ISSN:2575-8454
Online Access:Get full text
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Summary:We prove a k^{-\Omega\left(\log \left(\varepsilon_{2}-\varepsilon_{1}\right)\right)} lower bound for adap- tively testing whether a Boolean function is \varepsilon_{1}-close to or \varepsilon_{2}- far from k-juntas. Our results provide the first superpolynomial separation between tolerant and non-tolerant testing for a natural property of boolean functions under the adaptive setting. Furthermore, our techniques generalize to show that adaptively testing whether a function is \varepsilon_{1}-close to a k-junta or \varepsilon_{2}-far from (k+o(k))-juntas cannot be done with poly (k,\left(\varepsilon_{2}-\varepsilon_{1}\right)^{-1}) queries. This is in contrast to an algorithm by Iyer, Tal and Whitmeyer [CCC 2021] which uses poly (k,\left(\varepsilon_{2}-\varepsilon_{1}\right)^{-1}) queries to test whether a function is \varepsilon_{1}-close to a k-junta or \varepsilon_{2}-far from O(k /\left(\varepsilon_{2}-\varepsilon_{1}\right)^{2})-juntas
ISSN:2575-8454
DOI:10.1109/FOCS57990.2023.00108