This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
2011 26th Annual IEEE Conference on Computational Complexity
Property Testing Lower Bounds via Communication Complexity
San Jose, California USA
June 08-June 11
ISBN: 978-0-7695-4411-3
We develop a new technique for proving lower bounds in property testing, by showing a strong connection between testing and communication complexity. We give a simple scheme for reducing communication problems to testing problems, thus allowing us to use known lower bounds in communication complexity to prove lower bounds in testing. This scheme is general and implies a number of new testing bounds, as well as simpler proofs of several known bounds. For the problem of testing whether a boolean function is k-linear (a parity function on k variables), we achieve a lower bound of Omega(k) queries, even for adaptive algorithms with two-sided error, thus confirming a conjecture of Goldreich (2010). The same argument behind this lower bound also implies a new proof of known lower bounds for testing related classes such as k-juntas. For some classes, such as the class of monotone functions and the class of s-sparse GF(2) polynomials, we significantly strengthen the best known bounds.
Citation:
Eric Blais, Joshua Brody, Kevin Matulef, "Property Testing Lower Bounds via Communication Complexity," ccc, pp.210-220, 2011 26th Annual IEEE Conference on Computational Complexity, 2011
Usage of this product signifies your acceptance of the Terms of Use.