Introduction to Geometrical and Topological Methods in Distributed Computing

Emmanuel Godard (LIS)

Summary

We will present a serie of classical and recent results using geometrical and topological methods in distributed computability.

In this first talk, we present how to define a meaningful topology on a set of distributed executions. Using simplicial complexes as geometrical complexes, more than abstract complexes, we obtain, through geometrization, a topology which is almost a standard, well known, topology. We will present some other related topologies, and also how infinite complexes appear quite naturally in distributed computing. We will also discuss why we seem to need a notion of geometrization which is different from the standard notion of geometric realization.

This setting will be developped in a second talk to obtain a simple topological characterization of colorless distributed computability.