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 -