Journal of Computer and System Sciences - Special issue on FOCS 2002
Improved Bounds for Testing Juntas
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
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
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
3-bit dictator testing: 1 vs. 5/8
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
On proximity oblivious testing
Proceedings of the forty-first annual ACM symposium on Theory of computing
Testing juntas nearly optimally
Proceedings of the forty-first annual ACM symposium on Theory of computing
Testing Fourier Dimensionality and Sparsity
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
A Hypergraph Dictatorship Test with Perfect Completeness
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Testing Computability by Width Two OBDDs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Property testing: a learning theory perspective
COLT'07 Proceedings of the 20th annual conference on Learning theory
Approximating the distance to monotonicity in high dimensions
ACM Transactions on Algorithms (TALG)
Lower bounds for testing triangle-freeness in Boolean functions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Distribution-free testing algorithms for monomials with a sublinear number of queries
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
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
A query efficient non-adaptive long code test with perfect completeness
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
SIAM Journal on Computing
Testing juntas: a brief survey
Property testing
Testing by implicit learning: a brief survey
Property testing
Invariance in property testing
Property testing
Query-efficient dictatorship testing with perfect completeness
Property testing
Testing juntas: a brief survey
Property testing
Testing by implicit learning: a brief survey
Property testing
Invariance in property testing
Property testing
Query-efficient dictatorship testing with perfect completeness
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
Representing boolean functions using polynomials: more can offer less
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part III
Efficient sample extractors for juntas with applications
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Proximity oblivious testing and the role of invariances
Studies in complexity and cryptography
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
Proximity oblivious testing and the role of invariances
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On Proximity-Oblivious Testing
SIAM Journal on Computing
Testing Fourier Dimensionality and Sparsity
SIAM Journal on Computing
Information Processing Letters
Testing computability by width-two OBDDs
Theoretical Computer Science
Nearly tight bounds for testing function isomorphism
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Testing computability by width-2 OBDDs where the variable order is unknown
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
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We consider the problem of determining whether a given function $f:{\{0,1\}}^n\to{\{0,1\}}$ belongs to a certain class of Boolean functions $\cal F$ or whether it is far from the class. More precisely, given query access to the function f and given a distance parameter $\epsilon$, we would like to decide whether $f \in \cal F$ or whether it differs from every $g\in \cal F$ on more than an $\epsilon$-fraction of the domain elements. The classes of functions we consider are singleton ("dictatorship") functions, monomials, and monotone disjunctive normal form functions with a bounded number of terms. In all cases we provide algorithms whose query complexity is independent of n (the number of function variables), and linear in $1/\epsilon$.