TY - CHAP T1 - Distribution-Free Testing Lower Bounds for Basic Boolean Functions T2 - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques Y1 - 2007 A1 - Dana Dachman-Soled A1 - Servedio, Rocco A. ED - Charikar, Moses ED - Jansen, Klaus ED - Reingold, Omer ED - Rolim, José D. P. KW - Algorithm Analysis and Problem Complexity KW - Discrete Mathematics in Computer Science KW - Numeric Computing AB - In the distribution-free property testing model, the distance between functions is measured with respect to an arbitrary and unknown probability distribution \mathcal{D} over the input domain. We consider distribution-free testing of several basic Boolean function classes over {0,1} n , namely monotone conjunctions, general conjunctions, decision lists, and linear threshold functions. We prove that for each of these function classes, Ω((n/logn)1/5) oracle calls are required for any distribution-free testing algorithm. Since each of these function classes is known to be distribution-free properly learnable (and hence testable) using Θ(n) oracle calls, our lower bounds are within a polynomial factor of the best possible. JA - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques T3 - Lecture Notes in Computer Science PB - Springer Berlin Heidelberg SN - 978-3-540-74207-4, 978-3-540-74208-1 UR - http://link.springer.com/chapter/10.1007/978-3-540-74208-1_36 ER -