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A characterization of easily testable induced subgraphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The difficulty of testing for isomorphism against a graph that is given in advance
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A lower bound for testing juntas
Information Processing Letters
Learning functions of k relevant variables
Journal of Computer and System Sciences - Special issue: STOC 2003
A combinatorial characterization of the testable graph properties: it's all about regularity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A Characterization of Easily Testable Induced Subgraphs
Combinatorics, Probability and Computing
Information theory in property testing and monotonicity testing in higher dimension
Information and Computation
Quantum Algorithms for Learning and Testing Juntas
Quantum Information Processing
Distribution-Free Testing Lower Bounds for Basic Boolean Functions
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Attribute estimation and testing quasi-symmetry
Information Processing Letters
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
SIAM Journal on Computing
Testing (subclasses of) halfspaces
Property testing
Testing (subclasses of) halfspaces
Property testing
Efficient sample extractors for juntas with applications
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Information theory in property testing and monotonicity testing in higher dimension
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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We show that a Boolean function over n Boolean variables can be tested for the property of depending on only k of them, using a number of queries that depends only on k and the approximation parameter \varepsilon. We present two tests, both non-adaptive, that require a number of queries that is polynomial k and linear in \varepsilon ^{- 1}. The first test is stronger in that it has a 1-sided error, while the second test has a more compact analysis. We also present an adaptive version and a 2-sided error version of the first test, that have a somewhat better query complexity than the other algorithms.We then provide a lower bound of \bar \Omega (\sqrt k) on the number of queries required for the non-adaptive testing of the above property; a lower bound of \Omega (\log (k + 1)) for adaptive algorithms naturally follows from this. In providing this we also prove a result about random walks on the group {\rm Z}_2^9 that may be interesting in its own right. We show that for some t(q) = \bar 0(q^2) the distributions of the random walk at times t and t + 2 are close to each other, independently of the step distribution of the walk.We also discuss related questions. In particular, when given in advance a known k-junta function h, we show how to test a function f for the property of being identical to h up to a permutation of the variables, in a number of queries that is polynomial in k and \varepsilon.