Concurrent Kleene Algebra and its Foundations

erschienen 2011 in Journal of Logic and Algebraic Programming 80, pp. 266–296, 2011.

Abstract:
A Concurrent Kleene Algebra offers two composition operators, related by a weak version of an exchange law: when applied in a trace model of program semantics, one of them that stands for sequential execution and the other for concurrent execution of program components. After introducing this motivating concrete application, we investigate its abstract background in terms of a primitive independence relation between the traces. On this basis, we develop a series of richter algebras: the richest validates a proof calculus for programs similar to that of a Jones style rely/guarantee calculus. On the basis of this abstract algebra, we finally reconstruct the original trace model, using the notion of atoms from lattice theory.

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