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Proof labeling schemes

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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 algorithms- one 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 costly sometimes, since the configuration is typically generated so as to be easily verifiable. In contrast, our approach separates the configuration design from the verification. That is, it first generates the desired configuration without bothering with the need to verify it, and then handles the task of constructing a suitable verification scheme. Our approach thus allows for a more modular design of algorithms, and has the potential to aid in verifying properties even when the original design of the structures for maintaining them was done without verification in mind.

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Authors and Affiliations

  1. CNRS and University, Paris Diderot, Paris, 75013, France

    Amos Korman

  2. Information Systems Group, Faculty of IE and M, The Technion, 32000, Haifa, Israel

    Shay Kutten

  3. Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, 76100, Rehovot, Israel

    David Peleg

Authors
  1. Amos Korman
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  2. Shay Kutten
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  3. David Peleg
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Correspondence to Amos Korman.

Additional 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.

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Korman, A., Kutten, S. & Peleg, D. Proof labeling schemes. Distrib. Comput. 22, 215–233 (2010). https://doi.org/10.1007/s00446-010-0095-3

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