Higher dimensional automata revisited
نویسنده
چکیده
The dual of a true concurrency schedule appears to be a false concurrency automaton, a paradox we resolved in a previous paper by extending the latter to higher dimensions. This extension may be formalized via such discrete geometries as n-categories, simplicial complexes, cubical complexes, and Chu spaces. We advocate the last as having a clear notion of event, a well-defined process algebra uniformly extending that for event structures, and ease of extension beyond the basic before-during-after analysis.
منابع مشابه
The function ring functors of pointfree topology revisited
This paper establishes two new connections between the familiar function ring functor ${mathfrak R}$ on the category ${bf CRFrm}$ of completely regular frames and the category {bf CR}${mathbf sigma}${bf Frm} of completely regular $sigma$-frames as well as their counterparts for the analogous functor ${mathfrak Z}$ on the category {bf ODFrm} of 0-dimensional frames, given by the integer-valued f...
متن کاملHomology of Higher Dimensional Automata
Higher dimensional automata can model concurrent computations. The topological structure of the higher dimensional automata determines certain properties of the concurrent computation. We introduce bi-complexes as an algebraic tool for describing these automata and develop a simple homology theory for higher dimensional automata. We then show how the homology of automata has applications in the...
متن کاملHigher-Dimensional Timed Automata
We introduce a new formalism of higher-dimensional timed automata, based on van Glabbeek’s higher-dimensional automata and Alur’s timed automata. We prove that their reachability is PSPACE-complete and can be decided using zone-based algorithms. We also show how to use tensor products to combat state-space explosion and how to extend the setting to higher-dimensional hybrid automata.
متن کاملHomotopy Bisimilarity for Higher-Dimensional Automata
We introduce a new category of higher-dimensional automata in which the morphisms are functional homotopy simulations, i.e. functional simulations up to concurrency of independent events. For this, we use unfoldings of higher-dimensional automata into higher-dimensional trees. Using a notion of open maps in this category, we define homotopy bisimilarity. We show that homotopy bisimilarity is eq...
متن کاملHistory-Preserving Bisimilarity for Higher-Dimensional Automata via Open Maps
We show that history-preserving bisimilarity for higher-dimensional automata has a simple characterization directly in terms of higher-dimensional transitions. This implies that it is decidable for finite higher-dimensional automata. To arrive at our characterization, we apply the open-maps framework of Joyal, Nielsen and Winskel in the category of unfoldings of precubical sets.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Mathematical Structures in Computer Science
دوره 10 شماره
صفحات -
تاریخ انتشار 2000