Model-Checking One-Clock Priced Timed Automata

We consider the model of priced (a.k.a. weighted) timed automata, an extension of timed automata with cost information on both locations and transitions, and we study various model-checking problems for that model based on extensions of classical temporal logics with cost constraints on modalities. We prove that, under the assumption that the model has only one clock, model-checking this class of models against the logic WCTL, CTL with cost-constrained modalities, is PSPACE-complete (while it has been shown undecidable as soon as the model has three clocks). We also prove that model-checking WMTL, LTL with cost-constrained modalities, is decidable only if there is a single clock in the model and a single stopwatch cost variable (i.e., whose slopes lie in {0, 1}). An interesting direction of real-time model-checking that has recently received substantial attention is the extension and re-targeting of timed automata technology towards optimal scheduling and controller synthesis [AAM06, RLS04, BBL08]. In particular, scheduling problems can often be reformulated in terms of reachability questions with respect to behavioural models where tasks and resources relevant for the scheduling problem in question are modelled as interacting timed automata [BLR05a]. Although there exists a wide body of literature and established results on (optimal) scheduling in the fields of real-time systems and operations research, the application of model-checking has proved to provide a novel and competitive technology. In particular, model-checking has the advantage of offering a generic approach, going well beyond most classical scheduling solutions, which have good properties only for scenarios satisfying specific assumptions that may or, quite often, may not apply in actual practical circumstances. Of course, modelchecking comes with its own restrictions and stumbling blocks, the most notorious being 1998 ACM Subject Classification: F.1.1,F.3.1.