Cubes, homotopy and process algebra

Abstract

International audienceIn directed algebraic topology, the concurrent execution of n actions is abstracted by a full n-cube. Each coordinate corresponds to one of the n actions. This n-cube may be viewed as a representable presheaf of the category of precubical sets, as a topological n-cube equipped with some continuous paths modelling the possible execution paths up to homotopy, and as a commuting n-cube, i.e usually the small category associated with the poset of vertices of the n-cube. In fact, we have to remove the identity maps for various reasons, e.g., because the full n-cube does not contain any loop. In this talk, all these points of view are related to one another by considering Milner's calculus of communicating systems (CCS). All operators of this process algebra are given a higher dimensional interpretation. The restriction to dimension 1 corresponds to the usual structural operational semantics