Simplicial models for trace spaces {II}: {G}eneral higher dimensional automata

Abstract

Higher Dimensional Automata (HDA) are topological models for the study of concurrency phenomena. The state space for an HDA is given as a pre-cubical complex in which a set of directed paths (d-paths) is singled out. The aim of this paper is to describe a general method that determines the space of directed paths with given end points in a pre-cubical complex as the nerve of a particular category.

The paper generalizes the results from Raussen [Algebr. Geom. Topol. 10 (2010) 1683–1714; Appl. Algebra Engrg. Comm. Comput. 23 (2012) 59–84] in which we had to assume that the HDA in question arises from a semaphore model. In particular, important for applications, it allows for models in which directed loops occur in the processes involved.