Nondeterministic graph property testing

TL;DR

This paper proves that for dense graphs, nondeterministically testable properties, verified via certificates, are also deterministically testable, using graph limit theory to establish the equivalence.

Contribution

It demonstrates that nondeterministic testability implies deterministic testability for dense graph properties through the application of graph limit theory.

Findings

Nondeterministically testable properties are also deterministically testable.

Certificates can be unary and/or binary relations on nodes.

The proof uses the theory of graph limits.

Abstract

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 paper we study 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.