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
A Characterization of the (Natural) Graph Properties Testable with One-Sided Error
SIAM Journal on Computing
A separation theorem in property testing
Combinatorica
Relational properties expressible with one universal quantifier are testable
SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
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 between structures that have some desired property and those that are far from having the property, after examining only a small, random sample of the structure. We focus on the classification of first-order sentences based on their quantifier prefixes and vocabulary into testable and untestable classes. This classification was initiated by Alon et al. [1], who showed that graph properties expressible with quantifier patterns ∃*∀* are testable but that there is an untestable graph property expressible with quantifier pattern ∀*∃*. In the present paper, their untestable example is simplified. In particular, it is shown that there is an untestable graph property expressible with each of the following quantifier patterns: ∀∃∀∃, ∀∃∀2, ∀2∃∀ and ∀3∃.