Standard protocol complexes for the immediate snapshot read/write model

In this paper we consider a family of abstract simplicial complexes which we call immediate snapshot complexes. Their definition is motivated by theoretical distributed computing. Specifically, these complexes appear as protocol complexes in the general immediate snapshot execution model. In order to define and to analyze the immediate snapshot complexes we use the novel language of witness structures. We develop the rigorous mathematical theory of witness structures and use it to prove several combinatorial as well as topological properties of the immediate snapshot complexes. In particular, we prove that these complexes are simplicially homeomorphic to simplices.