Source: Logic, Language, Information and Computation,
Abstract. Property testing is a kind of randomized approximation in which one takes a small, random sample of a structure and wishes to determine whether the structure satisfies some property or is far from satisfying the property. We focus on the testability of classes of first-order expressible properties, and in particular, on the classification of prefix-vocabulary classes for testability. The main result is the untestability of [∀∃∀,(0,1)]=. This is a well-known class and minimal for untestability. We discuss what is currently known about the classification for testability and briefly compare it to other classifications.
Keywords: property testing, logic, randomized algorithms.
1 Supported by a Grant-in-Aid for JSPS Fellows under Grant No. 2100195209.
2 Supported by MEXT Grant-in-Aid for Scientific Research on Priority Areas under Grant No. 21013001.
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