An automata-theoretic approach to constraint LTL

We consider an extension of linear-time temporal logic (LTL) with constraints interpreted over a concrete domain. We use a new automata-theoretic technique to show PSPACE decidability of the logic for the constraint systems ( Z , < , = ) and ( N , < , = ). Along the way, we give an automata-theoretic proof of a result of Balbiani and Condotta when the constraint system satisfies the completion property. Our decision procedures extend easily to handle extensions of the logic with past-time 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 considers constraint systems that allow a counting mechanism.