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On Approximating the Number of Relevant Variables in a Function

Published:01 July 2013Publication History
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Abstract

In this work we consider the problem of approximating the number of relevant variables in a function given query access to the function. Since obtaining a multiplicative factor approximation is hard in general, we consider several relaxations of the problem. In particular, we consider a relaxation of the property testing variant of the problem and we consider relaxations in which we have a promise that the function belongs to a certain family of functions (e.g., linear functions). In the former relaxation the task is to distinguish between the case that the number of relevant variables is at most k, and the case in which it is far from any function in which the number of relevant variables is more than (1 + γ)k for a parameter γ. We give both upper bounds and almost matching lower bounds for the relaxations we study.

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          • Published in

            cover image ACM Transactions on Computation Theory
            ACM Transactions on Computation Theory  Volume 5, Issue 2
            July 2013
            104 pages
            ISSN:1942-3454
            EISSN:1942-3462
            DOI:10.1145/2493246
            Issue’s Table of Contents

            Copyright © 2013 ACM

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            Association for Computing Machinery

            New York, NY, United States

            Publication History

            • Published: 1 July 2013
            • Accepted: 1 March 2013
            • Revised: 1 June 2012
            • Received: 1 November 2011
            Published in toct Volume 5, Issue 2

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