期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2011
卷号：2011
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：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 relaxations in which we have a promise that the function belongs to a certain family of functions (e.g., linear functions), and we consider a relaxation of the property testing variant of the problem. In the latter 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 variable is more than (1+)k for a parameter . We give both upper bounds and almost matching lower bounds for the relaxations we study.
