| |
VOLUME 1, ISSUE 1, PAPER 1
|
Labelled transition systems as a Stone space
|
©Michael R. A. Huth, Department of Computing, Imperial College London
|
Abstract
A fully abstract and universal domain model for modal transition systems and
refinement is shown to be a maximal-points space model for the bisimulation
quotient of labelled transition systems over a finite set of events. In this
domain model we prove that this quotient is a Stone space whose compact,
zero-dimensional, and ultra-metrizable Hausdorff topology measures the degree
of bisimilarity such that image-finite labelled transition systems are dense.
Using this compactness we show that the set of labelled transition systems that
refine a modal transition system, its ''set of implementations'', is compact
and derive a compactness theorem for Hennessy-Milner logic on such
implementation sets. These results extend to systems that also have partially
specified state propositions, unify existing denotational, operational, and
metric semantics on partial processes, render robust consistency measures for
modal transition systems, and yield an abstract interpretation of compact sets
of labelled transition systems as Scott-closed sets of modal transition
systems.
|
Publication date: January 26, 2005
Full Text: PDF | PostScript
DOI: 10.2168/LMCS-1(1:1)2005
Hit Counts: 6061 |
 Creative Commons | |
