Foundations of Concurrent Kleene Algebra

Authors:
C. A. Hoare;Bernhard Möller;Georg Struth;Ian Wehrman
Affiliations:
Microsoft Research, Cambridge, UK;Universität Augsburg, Germany;University of Sheffield, UK;University of Texas at Austin, USA
Venue:
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Year:
2009

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Abstract

A Concurrent Kleene Algebra offers two composition operators, one that stands for sequential execution and the other for concurrent execution [10]. In this paper we investigate the abstract background of this law in terms of independence relations on which a concrete trace model of the algebra is based. Moreover, we show the interdependence of the basic properties of such relations and two further laws that are essential in the application of the algebra to a Jones style rely/guarantee calculus. Finally we reconstruct the trace model in a more abstract setting based on the notion of atoms from lattice theory.