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Geometric and combinatorial views on asynchronous computability

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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.

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Authors and Affiliations

  1. LIX, École Polytechnique, CNRS, Université Paris-Saclay, 91128, Palaiseau Cedex, France

    Éric Goubault & Samuel Mimram

  2. IRIF, Université Paris-Diderot, CNRS, Université Sorbonne Paris Cité, Paris, France

    Christine Tasson

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  1. Éric Goubault
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  2. Samuel Mimram
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  3. Christine Tasson
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Correspondence to Éric Goubault.

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Goubault, É., Mimram, S. & Tasson, C. Geometric and combinatorial views on asynchronous computability. Distrib. Comput. 31, 289–316 (2018). https://doi.org/10.1007/s00446-018-0328-4

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  • DOI: https://doi.org/10.1007/s00446-018-0328-4

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