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2012 Simplicial models for trace spaces {II}: {G}eneral higher dimensional automata
Martin Raussen
Algebr. Geom. Topol. 12(3): 1741-1761 (2012). DOI: 10.2140/agt.2012.12.1741


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.


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Martin Raussen. "Simplicial models for trace spaces {II}: {G}eneral higher dimensional automata." Algebr. Geom. Topol. 12 (3) 1741 - 1761, 2012.


Received: 13 September 2011; Accepted: 7 April 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1251.55004
Digital Object Identifier: 10.2140/agt.2012.12.1741

Primary: 55P10 , 55P15 , 55U10
Secondary: 68Q55 , 68Q85

Keywords: Arc length , covering , directed loop , execution path , higher dimensional automata , homotopy equivalence , poset category

Rights: Copyright © 2012 Mathematical Sciences Publishers


Vol.12 • No. 3 • 2012
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