On the Complexity of Nondeterministically Testable Hypergraph Parameters

TL;DR

This paper demonstrates that for uniform dense hypergraphs of any order, nondeterministic and deterministic testing of parameters and properties are equivalent, extending previous graph results to hypergraphs using advanced regularity and ultralimit techniques.

Contribution

It generalizes the equivalence of nondeterministic and deterministic testing from simple graphs to hypergraphs of arbitrary order, solving an open problem in hypergraph property testing.

Findings

Proves equivalence of nondeterministic and deterministic parameter testing for hypergraphs.

Establishes equivalence of nondeterministic and deterministic property testing for hypergraphs.

Introduces a new hypergraph cut norm and employs regularity and ultralimit methods.

Abstract

The paper proves the equivalence of the notions of nondeterministic and deterministic parameter testing for uniform dense hypergraphs of arbitrary order. It generalizes the result previously known only for the case of simple graphs. By a similar method we establish also the equivalence between nondeterministic and deterministic hypergraph property testing, answering the open problem in the area. We introduce a new notion of a cut norm for hypergraphs of higher order, and employ regularity techniques combined with the ultralimit method.