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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| Vydáno v: | Proceedings / annual Symposium on Foundations of Computer Science s. 1778 - 1786 |
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06.11.2023
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| ISSN: | 2575-8454 |
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| Abstract | 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 |
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| AbstractList | 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 |
| Author | Chen, Xi Patel, Shyamal |
| Author_xml | – sequence: 1 givenname: Xi surname: Chen fullname: Chen, Xi email: xichen@cs.columbia.edu organization: Columbia University,Department of Computer Science,New York,NY,USA – sequence: 2 givenname: Shyamal surname: Patel fullname: Patel, Shyamal email: shyamalpatelb@gmail.com organization: Columbia University,Department of Computer Science,New York,NY,USA |
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| Snippet | 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... |
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| StartPage | 1778 |
| SubjectTerms | Boolean functions Computer science Juntas Property Testing Sublinear Algorithms Testing Tolerant Testing |
| Title | New Lower Bounds for Adaptive Tolerant Junta Testing |
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