The critical complexity of all (monotone) Boolean functions and monotone graph properties
Information and Control
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Testing problems with sublearning sample complexity
Journal of Computer and System Sciences
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Testing the diameter of graphs
Random Structures & Algorithms
SIAM Journal on Discrete Mathematics
A lower bound for testing juntas
Information Processing Letters
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
Testing juntas nearly optimally
Proceedings of the forty-first annual ACM symposium on Theory of computing
Strong Lower Bounds for Approximating Distribution Support Size and the Distinct Elements Problem
SIAM Journal on Computing
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
Proceedings of the forty-third annual ACM symposium on Theory of computing
Testing Symmetric Properties of Distributions
SIAM Journal on Computing
Property Testing Lower Bounds via Communication Complexity
Computational Complexity - Selected papers from the 26th Annual IEEE Conference on Computational Complexity (CCC 2011)
Approximating the Influence of Monotone Boolean Functions in O(√n) Query Complexity
ACM Transactions on Computation Theory (TOCT)
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In this work we consider the problem of approximating the number of relevant variables in a function given query access to the function. Since obtaining a multiplicative factor approximation is hard in general, we consider several relaxations of the problem. In particular, we consider a relaxation of the property testing variant of the problem and we consider relaxations in which we have a promise that the function belongs to a certain family of functions (e.g., linear functions). In the former relaxation the task is to distinguish between the case that the number of relevant variables is at most k, and the case in which it is far from any function in which the number of relevant variables is more than (1 + γ)k for a parameter γ. We give both upper bounds and almost matching lower bounds for the relaxations we study.