## Abstract

This paper addresses the problem of locally verifying global properties. Several natural questions are studied, such as "how expensive is local verification?" and more specifically, "how expensive is local verification compared to computation?" A suitable model is introduced in which these questions are studied in terms of the number of bits a vertex needs to communicate. The model includes the definition of a proof labeling scheme (a pair of algorithmsone to assign the labels, and one to use them to verify that the global property holds). In addition, approaches are presented for the efficient construction of schemes, and upper and lower bounds are established on the bit complexity of schemes for multiple basic problems. The paper also studies the role and cost of unique identities in terms of impossibility and complexity, in the context of proof labeling schemes. Previous studies on related questions deal with distributed algorithms that simultaneously compute a configuration and verify that this configuration has a certain desired property. It turns out that this combined approach enables the verification to be less

Original language | English |
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Pages (from-to) | 215-233 |

Number of pages | 19 |

Journal | Distributed Computing |

Volume | 22 |

Issue number | 4 |

DOIs | |

State | Published - May 2010 |

Externally published | Yes |

### Bibliographical note

Funding Information:A preliminary version of this paper appeared in Proceedings of ACM PODC 2005. A. Korman was Supported in part at the Technion by an Aly Kaufman fellowship. S. Kutten was Supported in part by a grant from the Israel Science Foundation. D. Peleg was Supported in part by a grant from the Israel Science Foundation.

### Funding

A preliminary version of this paper appeared in Proceedings of ACM PODC 2005. A. Korman was Supported in part at the Technion by an Aly Kaufman fellowship. S. Kutten was Supported in part by a grant from the Israel Science Foundation. D. Peleg was Supported in part by a grant from the Israel Science Foundation.

Funders | Funder number |
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Israel Science Foundation |

## Keywords

- Distributed networks
- Proof labels
- Property verification
- Self stabilization