We consider an extension of linear-time temporal logic (LTL) with constraints interpreted over a concrete domain. We use a new automatatheoretic technique to show pspace decidability of the logic for the constraint systems (Z; =) and (N; =). Along the way, we give an automatatheoretic proof of a result of [BC02] when the constraint system D satises the completion property. Our decision procedures extend easily to handle extensions of the logic with past operators and constants, as well as an extension of the temporal language itself to monadic second order logic. Finally we show that the logic becomes undecidable when one consider constraint systems that allow a counting mechanism.
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