### 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 2013 |

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### ASJC Scopus subject areas

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

### Cite this

*Combinatorics Probability and Computing*,

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

**Non-deterministic graph property testing.** / Lovász, L.; Vesztergombi, Katalin.

Research output: Contribution to journal › Article

*Combinatorics Probability and Computing*, vol. 22, no. 5, pp. 749-762. https://doi.org/10.1017/S0963548313000205

}

TY - JOUR

T1 - Non-deterministic graph property testing

AU - Lovász, L.

AU - Vesztergombi, Katalin

PY - 2013/9

Y1 - 2013/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84881457015&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84881457015&partnerID=8YFLogxK

U2 - 10.1017/S0963548313000205

DO - 10.1017/S0963548313000205

M3 - Article

AN - SCOPUS:84881457015

VL - 22

SP - 749

EP - 762

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

SN - 0963-5483

IS - 5

ER -