A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on 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
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Testing membership in parenthesis languages
Random Structures & Algorithms
A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Three theorems regarding testing graph properties
Random Structures & Algorithms
Some 3CNF Properties Are Hard to Test
SIAM Journal on Computing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A combinatorial characterization of the testable graph properties: it's all about regularity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Every minor-closed property of sparse graphs is testable
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Space Complexity Vs. Query Complexity
Computational Complexity
Every Monotone Graph Property Is Testable
SIAM Journal on Computing
Studies in complexity and cryptography
Introduction to testing graph properties
Studies in complexity and cryptography
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Inflatable graph properties and natural property tests
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
A nearly-quadratic gap between adaptive and non-adaptive property testers
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
SIAM Journal on Discrete Mathematics
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Referring to the query complexity of property testing, we prove the existence of a rich hierarchy of corresponding complexity classes. That is, for any relevant function q , we prove the existence of properties that have testing complexity ***(q ). Such results are proven in three standard domains often considered in property testing: generic functions, adjacency predicates describing (dense) graphs, and incidence functions describing bounded-degree graphs. While in two cases the proofs are quite straightforward, the techniques employed in the case of the dense graph model seem significantly more involved. Specifically, problems that arise and are treated in the latter case include (1) the preservation of distances between graph under a blow-up operation, and (2) the construction of monotone graph properties that have local structure.