Timed Automata with Periodic Clock Constraints

The traditional constraints on the clocks of a timed automaton are based on real intervals, e. g., the value of a clock belongs to the interval (0; 1). Here, we introduce a new set of constraints, which we call \periodic", and which are based on regularly repeated real intervals, e. g., the value modulo 2 of a clock belongs to the interval (0; 1) which means that it belongs to (0; 1) or (2; 3) or (4; 5) .. .. Automata with these new constraints have greater expressive power than the au-tomata with traditional sets while satissability remains decidable. We address questions concerning-moves: simulation of automata with periodic constraints by au-tomata with traditional constraints and removal of-moves under certain conditions. Then, we enrich our model by introducing \count-down" clocks and show that the expressive power is not increased. Finally, we study three special cases: 1) all transitions reset clocks, 2) no transition reset clocks, and 3) the time domain is discrete and prove the decidability of the inclusion problem under each of these hypotheses.