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Counting-Based Impossibility Proofs for Renaming and Set Agreement

  • Hagit Attiya
  • Ami Paz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7611)

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.

Keywords

Prime Power Order Preserve Impossibility Result Colored Task Unique Permutation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hagit Attiya
    • 1
  • Ami Paz
    • 1
  1. 1.Department of Computer ScienceTechnionIsrael

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