From Geometric Semantics to Asynchronous Computability

Éric Goubault (1) , Samuel Mimram (1) , Christine Tasson (2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 PPS

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.

Domains: Distributed, Parallel, and Cluster Computing [cs.DC]

Éric Goubault, Samuel Mimram, Christine Tasson. From Geometric Semantics to Asynchronous Computability. DISC 2015, Toshimitsu Masuzawa; Koichi Wada, Oct 2015, Tokyo, Japan. ⟨10.1007/978-3-662-48653-5_29⟩. ⟨hal-01207146⟩