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A hierarchy of temporal properties (invited paper, 1989)

We propose a classification of temporal properties into a hierarchy. The classes of the hierarchy are characterized through four views: a language-theoretic view, a topologica1 view, the temporal logic view, and an automata view. In the topological view, the considered hierarchy coincides with the two lower levels of the Bore1 hierarchy, starting with the closed and open sets. For properties that are expressible by temporal logic and predicate automata, we provide a syntactic characterization of the formulae and automata that specify properties in the different classes. We relate this classification to the well known safety[iweness classification, and show that in some sense the two are orthogonal to one another.