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APPROX
2007
Springer

Distribution-Free Testing Lower Bounds for Basic Boolean Functions

9 years 20 days ago
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
Dana Glasner, Rocco A. Servedio
Added 07 Jun 2010
Updated 07 Jun 2010
Type Conference
Year 2007
Where APPROX
Authors Dana Glasner, Rocco A. Servedio
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