Abstract:It has been shown that for a dcpo P , the Scott closure of Γ c (P ) in Γ(P ) is a consistent Hoare powerdomain of P , where Γ c (P ) is the family of nonempty, consistent and Scott closed subsets of P , and Γ(P ) is the collection of all nonempty Scott closed subsets of P . In this paper, by introducing the notion of a −existing set, we present a direct characterization of the consistent Hoare powerdomain: the set of all −existing Scott closed subsets of a dcpo P is exactly the consistent Hoare powerdomain of … Show more
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