The decision problem for the probabilities of higher-order properties
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
0-1 laws and decision problems for fragments of second-order logic
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
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)
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
Testing the diameter of graphs
Random Structures & Algorithms
Ordered Paramodulation and Resolution as Decision Procedure
LPAR '93 Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning
0-1 Laws for Fragments of Existential Second-Order Logic: A Survey
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
ω-Regular languages are testable with a constant number of queries
Theoretical Computer Science
Testing graphs for colorability properties
Random Structures & Algorithms
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
A variant of the hypergraph removal lemma
Journal of Combinatorial Theory Series A
Regular Partitions of Hypergraphs: Regularity Lemmas
Combinatorics, Probability and Computing
Approximate Hypergraph Partitioning and Applications
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
A Characterization of the (Natural) Graph Properties Testable with One-Sided Error
SIAM Journal on Computing
A separation theorem in property testing
Combinatorica
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Testability and repair of hereditary hypergraph properties
Random Structures & Algorithms
Generalizations of the removal lemma
Combinatorica
Untestable properties in the kahr-moore-wang class
WoLLIC'11 Proceedings of the 18th international conference on Logic, language, information and computation
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In property testing, the goal is to distinguish structures that have some desired property from those that are far from having the property, based on only a small, random sample of the structure. We focus on the classification of first-order sentences according to their testability. This classification was initiated by Alon et al. (2000) [2], who showed that graph properties expressible with prefix @?^@?@?^@? are testable but that there is an untestable graph property expressible with quantifier prefix @?^@?@?^@?. The main results of the present paper are as follows. We prove that all (relational) properties expressible with quantifier prefix @?^@?@?@?^@? (Ackermann@?s class with equality) are testable and also extend the positive result of Alon et al. (2000) [2] to relational structures using a recent result by Austin and Tao (2010) [8]. Finally, we simplify the untestable property of Alon et al. (2000) [2] and show that prefixes @?^3@?, @?^2@?@?, @?@?@?^2 and @?@?@?@? can express untestable graph properties when equality is allowed.