Relational properties expressible with one universal quantifier are testable

Abstract

In property testing a small, random sample of an object is taken and one wishes to distinguish with high probability between the case where it has a desired property and the case where it is far from having the property. Much of the recent work has focused on graphs. In the present paper three generalized models for testing relational structures are introduced and relationships between these variations are shown. Furthermore, the logical classification problem for testability is considered and, as the main result, it is shown that Ackermann's class with equality is testable. © Springer-Verlag 2009.