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
The algorithmic aspects of the regularity lemma
Journal of Algorithms
Property testing in bounded degree graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Testing graphs for colorable properties
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
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
Regular Languages are Testable with a Constant Number of Queries
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
Testing the diameter of graphs
Random Structures & Algorithms
Testing membership in parenthesis languages
Random Structures & Algorithms
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Some 3CNF properties are hard to test
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Testing of function that have small width branching programs
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Three theorems regarding testing graph properties
Random Structures & Algorithms
Functions that have read-twice constant width branching programs are not necessarily testable
Random Structures & Algorithms
Abstract Combinatorial Programs and Efficient Property Testers
SIAM Journal on Computing
Every monotone graph property is testable
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Testing versus estimation of graph properties
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The Difficulty of Testing for Isomorphism against a Graph That Is Given in Advance
SIAM Journal on Computing
A Characterization of the (natural) Graph Properties Testable with One-Sided Error
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Graph limits and parameter testing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Property testing in hypergraphs and the removal lemma
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On testable properties in bounded degree graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Yet another algorithm for dense max cut: go greedy
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Comparing the strength of query types in property testing: the case of testing k-colorability
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Testing symmetric properties of distributions
STOC '08 Proceedings of the fortieth 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
Algebraic property testing: the role of invariance
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Space Complexity Vs. Query Complexity
Computational Complexity
Testing whether a digraph contains H-free k-induced subgraphs
Theoretical Computer Science
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
On the Randomness Complexity of Property Testing
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
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
Green's conjecture and testing linear-invariant properties
Proceedings of the forty-first annual ACM symposium on Theory of computing
Towards a Study of Low-Complexity Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Testing Fourier Dimensionality and Sparsity
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Hierarchy Theorems for Property Testing
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Algorithmic Aspects of Property Testing in the Dense Graphs Model
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
Indistinguishability and first-order logic
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Relational properties expressible with one universal quantifier are testable
SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
Property testing and parameter testing for permutations
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Lower bounds for testing triangle-freeness in Boolean functions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A brief introduction to property testing
Property testing
Introduction to testing graph properties
Property testing
Invariance in property testing
Property testing
Hierarchy theorems for property testing
Property testing
Algorithmic aspects of property testing in the dense graphs model
Property testing
A brief introduction to property testing
Property testing
Introduction to testing graph properties
Property testing
Invariance in property testing
Property testing
Hierarchy theorems for property testing
Property testing
Algorithmic aspects of property testing in the dense graphs model
Property testing
Every property of hyperfinite graphs is testable
Proceedings of the forty-third annual ACM symposium on Theory of computing
Review: Measuring instance difficulty for combinatorial optimization problems
Computers and Operations Research
Studies in complexity and cryptography
Proximity oblivious testing and the role of invariances
Studies in complexity and cryptography
A brief introduction to property testing
Studies in complexity and cryptography
Introduction to testing graph properties
Studies in complexity and cryptography
Contemplations on testing graph properties
Studies in complexity and cryptography
Characterizations of locally testable linear-and affine-invariant families
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On sums of locally testable affine invariant properties
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Limits on the rate of locally testable affine-invariant codes
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
Characterizations of locally testable linear- and affine-invariant families
Theoretical Computer Science
Algorithmic Aspects of Property Testing in the Dense Graphs Model
SIAM Journal on Computing
On Proximity-Oblivious Testing
SIAM Journal on Computing
Space complexity vs. query complexity
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
A nearly-quadratic gap between adaptive and non-adaptive property testers
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Testable and untestable classes of first-order formulae
Journal of Computer and System Sciences
A note on permutation regularity
Discrete Applied Mathematics
Every locally characterized affine-invariant property is testable
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
An algebraic characterization of testable boolean CSPs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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A common thread in recent results concerning the testing of dense graphs is the use of Szemerédi's regularity lemma. In this paper we show that in some sense this is not a coincidence. Our first result is that the property defined by having any given Szemerédi-partition is testable with a constant number of queries. Our second and main result is a purely combinatorial characterization of the graph properties that are testable with a constant number of queries. This characterization (roughly) says that a graph property P can be tested with a constant number of queries if and only if testing P can be reduced to testing the property of satisfying one of finitely many Szemerédi-partitions. This means that in some sense, testing for Szemerédi-partitions is as hard as testing any testable graph property. We thus resolve one of the main open problems in the area of property-testing, which was raised in the 1996 paper of Goldreich, Goldwasser and Ron [25] that initiated the study of graph property-testing. This characterization also gives an intuitive explanation as to what makes a graph property testable.