research-article

A characterization of locally testable affine-invariant properties via decomposition theorems

Author:

Yuichi YoshidaAuthors Info & Claims

STOC '14: Proceedings of the forty-sixth annual ACM symposium on Theory of computing

Pages 154 - 163

https://doi.org/10.1145/2591796.2591802

Published: 31 May 2014 Publication History

Abstract

Let P be a property of function Fⁿ^p → {0, 1} for a fixed prime p. An algorithm is called a tester for P if, given a query access to the input function f, with high probability, it accepts when f satisfies P and rejects when f is "far" from satisfying P. In this paper, we give a characterization of affine-invariant properties that are (two-sided error) testable with a constant number of queries. The characterization is stated in terms of decomposition theorems, which roughly claim that any function can be decomposed into a structured part that is a function of a constant number of polynomials, and a pseudo-random part whose Gowers norm is small. We first give an algorithm that tests whether the structured part of the input function has a specific form. Then we show that an affine-invariant property is testable with a constant number of queries if and only if it can be reduced to the problem of testing whether the structured part of the input function is close to one of a constant number of candidates.

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Cited By

CHIBA KITO H(2022)Sublinear Computation Paradigm: Constant-Time Algorithms and Sublinear Progressive AlgorithmsIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences10.1587/transfun.2021EAI0003E105.A:3(131-141)Online publication date: 1-Mar-2022
https://doi.org/10.1587/transfun.2021EAI0003
ITO HNAGAO APARK T(2019)Generalized Shogi, Chess, and Xiangqi are Constant-Time TestableIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences10.1587/transfun.E102.A.1126E102.A:9(1126-1133)Online publication date: 1-Sep-2019
https://doi.org/10.1587/transfun.E102.A.1126
Chen HYoshida YSuciu DSkritek SKoch C(2019)Testability of Homomorphism InadmissibilityProceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3294052.3319679(365-382)Online publication date: 25-Jun-2019
https://dl.acm.org/doi/10.1145/3294052.3319679
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Index Terms

A characterization of locally testable affine-invariant properties via decomposition theorems
1. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image ACM Conferences

STOC '14: Proceedings of the forty-sixth annual ACM symposium on Theory of computing

May 2014

984 pages

ISBN:9781450327107

DOI:10.1145/2591796

Program Chair:
David Shmoys
Cornell University

Copyright © 2014 ACM.

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 the author(s) 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: 31 May 2014

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Ministry of Education, Culture, Sports, Science, and Technology
Japan Society for the Promotion of Science
Japan Science and Technology Agency
Kawarabayashi Large Graph Project
ERATO

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STOC '14

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SIGACT

STOC '14: Symposium on Theory of Computing

May 31 - June 3, 2014

New York, New York

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STOC '14 Paper Acceptance Rate 91 of 319 submissions, 29%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

CHIBA KITO H(2022)Sublinear Computation Paradigm: Constant-Time Algorithms and Sublinear Progressive AlgorithmsIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences10.1587/transfun.2021EAI0003E105.A:3(131-141)Online publication date: 1-Mar-2022
https://doi.org/10.1587/transfun.2021EAI0003
ITO HNAGAO APARK T(2019)Generalized Shogi, Chess, and Xiangqi are Constant-Time TestableIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences10.1587/transfun.E102.A.1126E102.A:9(1126-1133)Online publication date: 1-Sep-2019
https://doi.org/10.1587/transfun.E102.A.1126
Chen HYoshida YSuciu DSkritek SKoch C(2019)Testability of Homomorphism InadmissibilityProceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3294052.3319679(365-382)Online publication date: 25-Jun-2019
https://dl.acm.org/doi/10.1145/3294052.3319679
Hayashi KYoshida Y(2019)Testing Proximity to Subspaces: Approximate $$\ell _\infty $$ ℓ ∞ Minimization in Constant TimeAlgorithmica10.1007/s00453-019-00642-0Online publication date: 25-Oct-2019
https://doi.org/10.1007/s00453-019-00642-0
Blais EYoshida Y(2018)A characterization of constant‐sample testable propertiesRandom Structures & Algorithms10.1002/rsa.2080755:1(73-88)Online publication date: 19-Sep-2018
https://doi.org/10.1002/rsa.20807
Hayashi KYoshida Y(2016)Minimizing quadratic functions in constant timeProceedings of the 30th International Conference on Neural Information Processing Systems10.5555/3157096.3157345(2225-2233)Online publication date: 5-Dec-2016
https://dl.acm.org/doi/10.5555/3157096.3157345
Yoshida Y(2016)Gowers norm, function limits, and parameter estimationProceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms10.5555/2884435.2884531(1391-1406)Online publication date: 10-Jan-2016
https://dl.acm.org/doi/10.5555/2884435.2884531
Oono KYoshida Y(2016)Testing properties of functions on finite groupsRandom Structures & Algorithms10.1002/rsa.2063949:3(579-598)Online publication date: 16-Feb-2016
https://doi.org/10.1002/rsa.20639

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