Untestable Properties in the Kahr-Moore-Wang Class

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 prefixvocabulary 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.