An automata-theoretic approach to constraint LTL

Stéphane Demri, Deepak D'Souza
2007 Information and Computation  
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
more » ... 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.
doi:10.1016/j.ic.2006.09.006 fatcat:f7djw6ovcfaflpfloy4ac4322i