### Abstract

A property of finite graphs is called non-deterministically 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 non-deterministically testable properties are also deterministically testable.

Original language | English |
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Pages (from-to) | 749-762 |

Number of pages | 14 |

Journal | Combinatorics Probability and Computing |

Volume | 22 |

Issue number | 5 |

DOIs | |

Publication status | Published - Sep 1 2013 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

Lovász, L., & Vesztergombi, K. (2013). Non-deterministic graph property testing.

*Combinatorics Probability and Computing*,*22*(5), 749-762. https://doi.org/10.1017/S0963548313000205