Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Self-testing/correcting for polynomials and for approximate functions
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Journal of the ACM (JACM)
On the efficiency of local decoding procedures for error-correcting codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
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
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
On the strength of comparisons in property testing
Information and Computation
Tolerant property testing and distance approximation
Journal of Computer and System Sciences
Information theory in property testing and monotonicity testing in higher dimension
Information and Computation
Estimating the distance to a monotone function
Random Structures & Algorithms
Parallel monotonicity reconstruction
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A Characterization of the (Natural) Graph Properties Testable with One-Sided Error
SIAM Journal on Computing
Testing monotonicity over graph products
Random Structures & Algorithms
Property-Preserving Data Reconstruction
Algorithmica
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity
SIAM Journal on Computing
Fast approximate PCPs for multidimensional bin-packing problems
Information and Computation
Approximating the distance to monotonicity in high dimensions
ACM Transactions on Algorithms (TALG)
Testability and repair of hereditary hypergraph properties
Random Structures & Algorithms
Local Monotonicity Reconstruction
SIAM Journal on Computing
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We propose a general model of local property reconstruction. Suppose we have a function f on domain Γ, which is supposed to have a particular property P, but may not have the property. We would like a procedure that produces a function g that has property P and is close to f (according to some suitable metric). The reconstruction procedure, called a filter, has the following form. The procedure takes as input an element x of Γ and outputs g(x). The procedure has oracle access to the function f and uses a single short random string ρ but is otherwise deterministic. This model was inspired by a related model of online property reconstruction that was introduced by by Ailon, Chazelle, Comandur and Liu (2004). It is related to the property testing model, and extends the framework that is used in the model of locally decodable codes. A similar model, in the context of hypergraph properties, was independently proposed and studied by Austin and Tao (2008). We specifically consider the property of monotonicity and develop an efficient local filter for this property. The input f is a real valued function defined over the domain {1, . . . ,n}d (where n is viewed as large and d as a constant). The function is monotone if the following property holds: for two domain elements x and y, if x ≤ y (in the product order) then f(x) ≤ f(y). Given x, our filter outputs the value g(x) in (log n)O(1) time and uses a random seed ρ of the same size. With high probability, the ratio of the Hamming distance between g and f to the minimum possible Hamming distance between a monotone function and f is bounded above by a function of d (independent of n).