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Closed schedulers: Constructions and applications to consensus protocols

  • Ronit Lubitch
  • Shlomo Moran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 647)

Abstract

Analyzing distributed protocols in various models often involves a careful analysis of the set of admissible runs, for which the protocols should behave correctly. In particular, the admissible runs assumed by a t-resilient protocol are runs which are fair for all but at most t processors. In this paper we define closed sets of runs, and suggest a technique to prove impossibility results for t-resilient protocols, by restricting the corresponding sets of admissible runs to smaller sets, which are closed, as follows:

For each protocol PR and for each initial configuration c, the set of admissible runs of PR which start from c defines a tree in a natural way: the root of the tree is the empty run, and each vertex in it denotes a finite prefix of an admissible run; a vertex u in the tree has a son v iff v is also a prefix of an admissible run, which extends u by one atomic step.

The tree of admissible runs described above may contain infinite paths which are not admissible runs. A set of admissible runs is closed if for every possible initial configuration c, each path in the tree of admissible runs starting from c is also an admissible run. Closed sets of runs have the simple combinatorial structure of the set of paths of an infinite tree, which makes them easier to analyze.

We introduce a unified method for constructing closed sets of admissible runs by using a model-independent construction of closed schedulers. We use this construction to provide unified proofs of impossibility results in various models of asynchronous computations. One of our results generalizes a known impossibility result in a non-trivial way.

Keywords

Initial Configuration Atomic Step Impossibility Result Consensus Protocol Infinite Path 
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 1992

Authors and Affiliations

  • Ronit Lubitch
    • 1
  • Shlomo Moran
    • 1
  1. 1.Dept. of Computer ScienceTechnionHaifaIsrael

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