Nondeterministic Property Testing

A property of finite graphs is called nondeterministically testable if it has a "certificate'' such that once the certificate is specified, its correctness can be verified by random local testing. In this talk we consider certificates that consist of one or more unary and/or binary relations on the nodes, in the case of dense graphs. Using the theory of graph limits, we prove that nondeterministically testable properties are also deterministically testable. In contrast, for bounded degree graphs the two classes are different. This is joint work with Kati Vesztergombi.