On Projective and Separable Properties

A language L over the Cartesian product of component alphabets is called projective if it is closed under projections. That is, together with each word α e L, it contains all the words that have the same projections up to stuttering as α. We prove that in each of the behavior classes: ω-regular, regular and star-free ω-regular (i.e., definable by linear temporal logic) languages, the projective languages are precisely the Boolean combinations of stuttering-closed component languages from the corresponding class. Languages of these behavior classes can also be seen as properties of various temporal logics; some uses of projective properties for specification and verification of programs are studied.

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