Abstract. Current approaches to monitoring real-time properties suffer either from unbounded space requirements or lack of expressiveness. In this paper, we adapt a separation technique enabling us to rewrite arbitrary MTL formulas into LTL formulas over a set of atoms comprising bounded MTL formulas. As a result, we obtain the first trace-length independent online monitoring procedure for full MTL.

Abstract. Consider a finite set of targets, with each target assigned a relative deadline, and each pair of targets assigned a fixed transit flight time. Given a flock of identical UAVs, can one ensure that every target is repeatedly visited by some UAV at intervals of duration at most the target's relative deadline? The Cyclic-Routing UAV Problem (cr-uav) is the question of whether this task has a solution. This problem can straightforwardly be solved in PSPACE by modelling it as a network of timed automata. The special case of there being a single UAV is claimed to be NP-complete in the literature. In this paper, we show that the cr-uav Problem is in fact PSPACE-complete even in the single-UAV case.

It is known that Metric Temporal Logic (MTL) is strictly less expressive than the Monadic First-Order Logic of Order and Metric (FO[<, +1]) in the pointwise semantics over bounded time domains (i.e., timed words of bounded duration) [2]. In this paper, we present an extension of MTL, relying on two new temporal operators 'Earlier' (E) and 'Newer' (N), which has the same expressive power as FO[<, +1] in both the pointwise and continuous semantics over bounded time domains.

It is known that Metric Temporal Logic (MTL) is strictly less expressive than the Monadic First-Order Logic of Order and Metric (FO[<, +1]) when interpreted over timed words; this remains true even when the time domain is bounded a priori. In this work, we present an extension of MTL with the same expressive power as FO[<, +1] over bounded timed words (and also, trivially, over time-bounded signals). We then show that expressive completeness also holds in the general (time-unbounded) case if we allow the use of rational constants q ∈ Q in formulas. This extended version of MTL therefore yields a definitive real-time analogue of Kamp's theorem. As an application, we propose a trace-length independent monitoring procedure for our extension of MTL, the first such procedure in a dense real-time setting.

Metric Interval Temporal Logic (MITL) is an extension of the classical Linear Time Logic (LTL) that can be used to characterise real-time properties of computer systems. While the practical interest of MITL is undeniable, there is still today a remarkable lack of tool support for this logic. In this short paper, we report on our ongoing work effort to complete the theoretical knowledge about MITL. We also report on our recently introduced tool MightyL, which translates MITL formulae into timed automata, enabling efficient modelchecking of this logic. Finally, we sketch the future directions of our current line of research, which will be to extend MightyL to support reactive synthesis of MITL properties.