Abstract
The main result of this article is that every demonic refinement algebra with enabledness and termination is isomorphic to an algebra of ordered pairs of elements of a Kleene algebra with domain and with a divergence operator satisfying a mild condition. Divergence is an operator producing a test interpreted as the set of states from which nontermination may occur. An example of a KAD where a divergence operator cannot be defined is given. In addition, it is shown that every demonic refinement algebra with enabledness is also a demonic refinement algebra with termination.
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