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A o(n) monotonicity tester for boolean functions over the hypercube

Published: 01 June 2013 Publication History

Abstract

Given oracle access to a Boolean function f:{0,1}n -> {0,1}, we design a randomized tester that takes as input a parameter ε>0, and outputs Yes if the function is monotonically non-increasing, and outputs No with probability >2/3, if the function is ε-far from being monotone, that is, f needs to be modified at ε-fraction of the points to make it monotone. Our non-adaptive, one-sided tester makes ~O(n5/6ε-5/3) queries to the oracle.

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  • (2023)An optimal tester for k-linearTheoretical Computer Science10.1016/j.tcs.2023.113759950:COnline publication date: 16-Mar-2023
  • (2022)Properly learning monotone functions via local correction2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS54457.2022.00015(75-86)Online publication date: Oct-2022
  • (2022)On Monotonicity Testing and the 2-to-2 Games ConjectureundefinedOnline publication date: 5-Dec-2022
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cover image ACM Conferences
STOC '13: Proceedings of the forty-fifth annual ACM symposium on Theory of Computing
June 2013
998 pages
ISBN:9781450320290
DOI:10.1145/2488608
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 June 2013

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Author Tags

  1. boolean functions
  2. boolean hypercube
  3. monotonicity
  4. property testing

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STOC'13
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STOC'13: Symposium on Theory of Computing
June 1 - 4, 2013
California, Palo Alto, USA

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STOC '13 Paper Acceptance Rate 100 of 360 submissions, 28%;
Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

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  • (2023)An optimal tester for k-linearTheoretical Computer Science10.1016/j.tcs.2023.113759950:COnline publication date: 16-Mar-2023
  • (2022)Properly learning monotone functions via local correction2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS54457.2022.00015(75-86)Online publication date: Oct-2022
  • (2022)On Monotonicity Testing and the 2-to-2 Games ConjectureundefinedOnline publication date: 5-Dec-2022
  • (2019)Almost optimal distribution-free junta testingProceedings of the 34th Computational Complexity Conference10.4230/LIPIcs.CCC.2019.2(1-13)Online publication date: 17-Jul-2019
  • (2018)Distribution-free Junta TestingACM Transactions on Algorithms10.1145/326443415:1(1-23)Online publication date: 24-Sep-2018
  • (2018)Settling the Query Complexity of Non-adaptive Junta TestingJournal of the ACM10.1145/321377265:6(1-18)Online publication date: 26-Nov-2018
  • (2018)Distribution-free junta testingProceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3188745.3188842(749-759)Online publication date: 20-Jun-2018
  • (2017)Settling the query complexity of non-adaptive junta testingProceedings of the 32nd Computational Complexity Conference10.5555/3135595.3135621(1-19)Online publication date: 9-Jul-2017
  • (2016)Communication Complexity for Algorithm DesignersFoundations and Trends® in Theoretical Computer Science10.1561/040000007611:3–4(217-404)Online publication date: 1-May-2016
  • (2016)A polynomial lower bound for testing monotonicityProceedings of the forty-eighth annual ACM symposium on Theory of Computing10.1145/2897518.2897567(1021-1032)Online publication date: 19-Jun-2016
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