Distributed Computing

, Volume 31, Issue 4, pp 289–316 | Cite as

Geometric and combinatorial views on asynchronous computability

  • Éric GoubaultEmail author
  • Samuel Mimram
  • Christine Tasson


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.


Fault-tolerant distributed computing Atomic snapshot protocol Protocol complex Directed algebraic topology Dihomotopy Interval order 


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.LIX, École Polytechnique, CNRSUniversité Paris-SaclayPalaiseau CedexFrance
  2. 2.IRIF, Université Paris-Diderot, CNRS, Université Sorbonne Paris CitéParisFrance

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