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From Geometric Semantics to Asynchronous Computability

  • Éric GoubaultEmail author
  • Samuel Mimram
  • Christine Tasson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9363)

Abstract

We show that the protocol complex formalization of fault-tolerant protocols can be directly derived from a suitable semantics of the underlying synchronization and communication primitives, based on a geometrization of the state space. By constructing a one-to-one relationship between simplices of the protocol complex and (di)homotopy classes of (di)paths in the latter semantics, we describe a connection between these two geometric approaches to distributed computing: protocol complexes and directed algebraic topology. This is exemplified on atomic snapshot, iterated snapshot and layered immediate snapshot protocols, where a well-known combinatorial structure, interval orders, plays a key role. We believe that this correspondence between models will extend to proving impossibility results for much more intricate fault-tolerant distributed architectures.

Keywords

Decision Task Simplicial Complex Local Memory Global Memory Interval Order 
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 2015

Authors and Affiliations

  • Éric Goubault
    • 1
    Email author
  • Samuel Mimram
    • 1
  • Christine Tasson
    • 2
  1. 1.LIXÉcole PolytechniquePalaiseauFrance
  2. 2.PPSUniversité ParisParisFrance

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