TY - CHAP
T1 - A Canonical Form for Testing Boolean Function Properties
T2 - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Y1 - 2011
A1 - Dana Dachman-Soled
A1 - Servedio, Rocco A.
ED - Goldberg, Leslie Ann
ED - Jansen, Klaus
ED - Ravi, R.
ED - Rolim, José D. P.
KW - Algorithm Analysis and Problem Complexity
KW - Boolean functions
KW - Computation by Abstract Devices
KW - Computer Communication Networks
KW - Computer Graphics
KW - Data structures
KW - Discrete Mathematics in Computer Science
KW - property testing
AB - In a well-known result Goldreich and Trevisan (2003) showed that every testable graph property has a “canonical” tester in which a set of vertices is selected at random and the edges queried are the complete graph over the selected vertices. We define a similar-in-spirit canonical form for Boolean function testing algorithms, and show that under some mild conditions property testers for Boolean functions can be transformed into this canonical form. Our first main result shows, roughly speaking, that every “nice” family of Boolean functions that has low noise sensitivity and is testable by an “independent tester,” has a canonical testing algorithm. Our second main result is similar but holds instead for families of Boolean functions that are closed under ID-negative minors. Taken together, these two results cover almost all of the constant-query Boolean function testing algorithms that we know of in the literature, and show that all of these testing algorithms can be automatically converted into a canonical form.
JA - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
T3 - Lecture Notes in Computer Science
PB - Springer Berlin Heidelberg
SN - 978-3-642-22934-3, 978-3-642-22935-0
UR - http://link.springer.com/chapter/10.1007/978-3-642-22935-0_39
ER -