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Counting-Based Impossibility Proofs for Renaming and Set Agreement

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Book cover Distributed Computing (DISC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7611))

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Abstract

Renaming and set agreement are two fundamental sub-consensus tasks. In the M-renaming task, processes start with names from a large domain and must decide on distinct names in a range of size M; in the k-set agreement task, processes must decide on at most k of their input values. Renaming and set agreement are representatives of the classes of colored and colorless tasks, respectively.

This paper presents simple proofs for key impossibility results for wait-free computation using only read and write operations: n processes cannot solve (n − 1)-set agreement, and, if n is a prime power, n processes cannot solve (2n − 2)-renaming.

Our proofs consider a restricted set of executions, and combine simple operational properties of these executions with elementary counting arguments, to show the existence of an execution violating the task’s requirements. This makes the proofs easier to understand, verify, and hopefully, extend.

This research is supported in part by Yad-HaNadiv fund and the Israel Science Foundation (grant number 1227/10).

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Authors and Affiliations

  1. Department of Computer Science, Technion, Israel

    Hagit Attiya & Ami Paz

Authors
  1. Hagit Attiya
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  2. Ami Paz
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Editors and Affiliations

  1. Microsoft Corporation, Building SVC6, 1065 La Avenida, 94043, Mountain View, CA, USA

    Marcos K. Aguilera

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Attiya, H., Paz, A. (2012). Counting-Based Impossibility Proofs for Renaming and Set Agreement. In: Aguilera, M.K. (eds) Distributed Computing. DISC 2012. Lecture Notes in Computer Science, vol 7611. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33651-5_25

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  • DOI: https://doi.org/10.1007/978-3-642-33651-5_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33650-8

  • Online ISBN: 978-3-642-33651-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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