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Journal of Computer and System Sciences
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Property testing and its connection to learning and approximation
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PCP characterizations of NP: towards a polynomially-small error-probability
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
The importance of being biased
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Monotonicity testing over general poset domains
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Testing Basic Boolean Formulae
SIAM Journal on Discrete Mathematics
Improved Testing Algorithms for Monotonicity
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Optimal Attribute-Efficient Learning of Disjunction, Parity and Threshold Functions
EuroCOLT '97 Proceedings of the Third European Conference on Computational Learning Theory
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Testing monotonicity over graph products
Random Structures & Algorithms
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
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
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
A local decision test for sparse polynomials
Information Processing Letters
Testing Boolean function isomorphism
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
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
Testing juntas: a brief survey
Property testing
Testing by implicit learning: a brief survey
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Testing juntas: a brief survey
Property testing
Testing by implicit learning: a brief survey
Property testing
Invariance in property testing
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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
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
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
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)
Testing linear-invariant function isomorphism
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We show that a boolean valued function over n variables, where each variable ranges in an arbitrary probability space, can be tested for the property of depending on only J of them using a number of queries that depends only polynomially on J and the approximation parameter ε. We present several tests that require a number of queries that is polynomial in J and linear in ε-1. We showa non-adaptive tests that has one-sided error, an adaptive version of it that requires fewer queries, and a non-adaptive two-sided version of the test that requires the least number of queries. We also show a two-sided non-adaptive test that applies to functions over n boolean variables, and has a more compact analysis.We then provide a lower bound of Ω˜(√J) on the number of queries required for the nonadaptive testing of the above property; a lower bound of Ω(log(J + 1)) for adaptive algorithms naturally follows from this. In establishing this lower bound we also prove a result about random walks on the group Z2q that may be interesting in its own right. We show that for some t(q) = Ω˜(q2), 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 J-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 J and ε-1.