Learning in the presence of finitely or infinitely many irrelevant attributes
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Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
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Testing Basic Boolean Formulae
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SIAM Journal on Computing
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Approximation Resistant Predicates from Pairwise Independence
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Gaussian Bounds for Noise Correlation of Functions and Tight Analysis of Long Codes
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
A local decision test for sparse polynomials
Information Processing Letters
Testing non-uniform k-wise independent distributions over product spaces
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
On testing computability by small width OBDDs
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
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APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Testing juntas: a brief survey
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Testing by implicit learning: a brief survey
Property testing
Invariance in property testing
Property testing
Property testing
Testing juntas: a brief survey
Property testing
Testing by implicit learning: a brief survey
Property testing
Invariance in property testing
Property testing
Property testing
Lower bounds for testing computability by small width OBDDs
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Efficient sample extractors for juntas with applications
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
A canonical form for testing boolean function properties
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Approximating the influence of monotone boolean functions in O(√n) query complexity
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On approximating the number of relevant variables in a function
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Testing Fourier Dimensionality and Sparsity
SIAM Journal on Computing
Information Processing Letters
Nearly tight bounds for testing function isomorphism
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Approximating the Influence of Monotone Boolean Functions in O(√n) Query Complexity
ACM Transactions on Computation Theory (TOCT)
On Approximating the Number of Relevant Variables in a Function
ACM Transactions on Computation Theory (TOCT)
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A function on n variables is called a k-junta if it depends on at most k of its variables. In this article, we show that it is possible to test whether a function is a k-junta or is "far" from being a k-junta with O(kε + k log k ) queries, where epsilon is the approximation parameter. This result improves on the previous best upper bound of O (k3/2)ε queries and is asymptotically optimal, up to a logarithmic factor. We obtain the improved upper bound by introducing a new algorithm with one-sided error for testing juntas. Notably, the algorithm is a valid junta tester under very general conditions: it holds for functions with arbitrary finite domains and ranges, and it holds under any product distribution over the domain. A key component of the analysis of the new algorithm is a new structural result on juntas: roughly, we show that if a function f is "far" from being a k-junta, then f is "far" from being determined by k parts in a random partition of the variables. The structural lemma is proved using the Efron-Stein decomposition method.