Distribution-Free Testing Lower Bounds for Basic Boolean Functions

: In the distribution-free property testing model, the distance between functions is measured with respect to an arbitrary and unknown probability distribution 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 polynomially related to the best possible. ACM Classification: F.2.2, G.3 AMS Classification: 68Q99, 68W20 Key words and phrases: property testing, distribution-free testing, decision list, conjunction, linear threshold function

• Type: Conference
• Year: 2007
• Where: APPROX
• Authors: Dana Glasner, Rocco A. Servedio
• Keywords: Algorithms, APPROX 2007, Distribution-free Testing, Function Classes, Linear Threshold Function