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ISSN (electronic): 1472-2739
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Simplicial models for trace spaces {II}: {G}eneral higher dimensional automata

Martin Raussen

Algebraic & Geometric Topology 12 (2012) 1741–1761

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.

higher dimensional automata, execution path, poset category, directed loop, arc length, covering, homotopy equivalence
Mathematical Subject Classification 2010
Primary: 55P10, 55P15, 55U10
Secondary: 68Q85, 68Q55
Received: 13 September 2011
Accepted: 7 April 2012
Published: 4 August 2012
Martin Raussen
Department of Mathematical Sciences
Aalborg University
Fredrik Bajersvej 7G
DK-9220 Aalborg Øst