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On Sample-Based Testers

Published:25 April 2016Publication History
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Abstract

The standard definition of property testing endows the tester with the ability to make arbitrary queries to “elements” of the tested object. In contrast, sample-based testers only obtain independently distributed elements (a.k.a. labeled samples) of the tested object. While sample-based testers were defined by Goldreich, Goldwasser, and Ron (JACM 1998), with few exceptions, most research in property testing has focused on query-based testers.

In this work, we advance the study of sample-based property testers by providing several general positive results as well as by revealing relations between variants of this testing model. In particular:

—We show that certain types of query-based testers yield sample-based testers of sublinear sample complexity. For example, this holds for a natural class of proximity oblivious testers.

—We study the relation between distribution-free sample-based testers and one-sided error sample-based testers w.r.t. the uniform distribution.

While most of this work ignores the time complexity of testing, one part of it does focus on this aspect. The main result in this part is a sublinear-time sample-based tester, in the dense graphs model, for k-colorability, for any k ⩾ 2.

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      • Published in

        cover image ACM Transactions on Computation Theory
        ACM Transactions on Computation Theory  Volume 8, Issue 2
        May 2016
        92 pages
        ISSN:1942-3454
        EISSN:1942-3462
        DOI:10.1145/2930059
        Issue’s Table of Contents

        Copyright © 2016 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 25 April 2016
        • Accepted: 1 February 2016
        • Revised: 1 October 2015
        • Received: 1 February 2015
        Published in toct Volume 8, Issue 2

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