Simplicial models for trace spaces II: General higher dimensional automata

Raussen, Martin

doi:10.2140/agt.2012.12.1741

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

Martin Raussen

Algebraic & Geometric Topology 12 (2012) 1741–1761

DOI: 10.2140/agt.2012.12.1741

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.

Keywords

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

References

Publication

Received: 13 September 2011

Accepted: 7 April 2012

Published: 4 August 2012

Authors

Martin Raussen
Department of Mathematical Sciences Aalborg University Fredrik Bajersvej 7G DK-9220 Aalborg Øst Denmark
http://people.math.aau.dk/~raussen

Volume 12, issue 3 (2012)