Higher dimensional transition systems
Gian Luca Cattani,Vladimiro Sassone +1 more
- pp 55-62
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TLDR
It is proved that the natural notion of bisimulation for such structures is a generalisation of the strong history preserving bisimulations, and an abstract categorical account of it via open maps is provided.Abstract:
We introduce the notion of higher dimensional transition systems as a model of concurrency providing an elementary, set-theoretic formalisation of the idea of higher dimensional transition. We show an embedding of the category of higher dimensional transition systems into that of higher dimensional automata which cuts down to an equivalence when we restrict to non-degenerate automata. Moreover, we prove that the natural notion of bisimulation for such structures is a generalisation of the strong history preserving bisimulation, and provide an abstract categorical account of it via open maps. Finally, we define a notion of unfolding for higher dimensional transition systems and characterise the structures so obtained as a generalisation of event structures.read more
Citations
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Journal ArticleDOI
Algebraic topology and concurrency
TL;DR: It is shown that some concepts from homotopy theory, in algebraic topology, are relevant for studying concurrent programs, and some of these concepts are applied to the proof of the safeness of a two-phase protocol, well-known and used in concurrent database theory.
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On the expressiveness of higher dimensional automata
TL;DR: This paper translates several models of concurrency into the model of higher dimensional automata (HDA), which is the most expressive model under investigation, and proposes four different translations of Petri nets corresponding to the four different computational interpretations of nets found in the literature.
Book ChapterDOI
Presheaf Models for Concurrency
Gian Luca Cattani,Glynn Winskel +1 more
TL;DR: One new result here is that a wide range of left Kan extensions, between categories of presheaves, preserve open maps, and this implies that any colimit-preserving functor between presheaf categories preserves open maps.
Journal ArticleDOI
Geometry and concurrency: a user's guide
TL;DR: Some of the main directions of research in concurrency theory are identified, and some of the major ideas on which all this is based are surveyed.
Journal ArticleDOI
Higher dimensional automata revisited
TL;DR: The dual of a true concurrency schedule appears to be a false concurrency automaton, a paradox resolved in a previous paper by extending the latter to higher dimensions by formalizing via such discrete geometries as n-categories, simplicial complexes, cubical complexes and Chu spaces.
References
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Book ChapterDOI
Models for concurrency
Glynn Winskel,Mogens Nielsen +1 more
TL;DR: In this article, the authors present a survey of models for parallel computation, including transition systems, synchronisation trees, Petri nets, event structures, pomsets and Mazurkiewicz traces.
Event structures
TL;DR: The mathematical theory of event structures is presented, how they are related to Petri nets and Scott domains, and how they can be used to provide semantics to programming languages for parallel processes as welt as languages with higher types are surveyed.
Journal ArticleDOI
Petri nets are moniods
José Meseguer,Ugo Montanari +1 more
TL;DR: A formal basis for expressing the semantics of concurrent languages in terms of Petri nets is provided, and a new understanding of concurrency in Terms of algebraic structures over graphs and categories is provided.
Journal ArticleDOI
Bisimulation from Open Maps
TL;DR: A logic, generalising Hennessy?Milner logic, which is characteristic for the generalised notion of bisimulation is presented, which makes possible a uniform definition of bisIMulation across a range of different models for parallel computation presented as categories.