An Automata-Theoretic Decision Procedure for Future Interval Logic
نویسندگان
چکیده
Graphical Interval Logic (GIL) is a temporal logic in which all reasoning is done by means of diagram-matic formull. It is a discrete linear-time modal logic in which the basic temporal modality is the interval. Future Interval Logic (FIL) provides the logical foundation for GIL. In this paper we present an automata-theoretic decision procedure for FIL with complexity DTIME(2 O(n k)), where n is the size of the formula and k is the depth of interval nesting. For formull with bounded depth but length unbounded, the satissability problem for FIL is shown to be PSPACE-complete. We believe that this is the rst result giving a direct decision procedure of elementary complexity for an interval logic. We also show that the logic is transparent to nite stuttering over the class of !-sequences, a feature that is useful for composition and reene-ment.
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