Some Notes on Duality in Refinement Algebra

erschienen 2006 in R. Schmidt, G. Struth (eds.): Relations and Kleene Algebra in Computer Science - PhD Programme (RelMiCS/AKA 06)
Research Report CS-06-09, Department of Computer Science, University of Sheffield
pp. 84-88, 2006.

Abstract:
We formulate a duality principle for refinement algebras. We first consider the dual of Kleene star: angelic iteration. Angelic iteration was introduced by Back, Mikhajlova and von Wright in a predicatetransformer setting, here we propose an abstract-algebraic characterisation. This allows us to formulate the duality principle. We conclude by considering iterative choice and by introducing the dual of action systems.