Foundations of Concurrent Kleene Algebra
C.A.R. Hoare, B. Möller, G. Struth and I. Wehrman
2009-05in: Universität Augsburg Technical Report, Institute of Computer Science, University of Augsburg, April 2009
A Concurrent Kleene Algebra offers two composition operators, one that stands for sequential execution and the other for concurrent execution. 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.
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