BibTeX
@TECHREPORT{Errington99twistedsystems,
author = {David Lindsay Errington},
title = {Twisted Systems},
institution = {},
year = {1999}
}
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Abstract
Let J be a shape in some category Shp for which there is a functor : Shp Cat. A categorical transition system (or system) is a pair (J; (J) C) consisting of a shape labelled by a functor in a category in C. Suitable choices for Shp include categories of partial orders, graphs, higher-dimensional automata and other structures with intrinsic notions of states and transitions. The construction yields a category CTS(Shp; C). Systems generalize conventional labelled transition systems over which they have some advantages. By abandoning graphs as shapes it becomes possible to model concurrent and asynchronous computation. By labelling in a category, rather than an alphabet or term algebra, the actions of an algorithm or process can have much richer structure. Actions can be functions, partial functions, machine instructions or even processes. Of particular importance are twisted systems. These have the form (J; ] (J) C) where g (\Gamma) : Cat Cat is the twisted arrow category constructi...
