Theoretical Computer Science
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
What's decidable about hybrid automata?
Journal of Computer and System Sciences
The Impressive Power of Stopwatches
CONCUR '00 Proceedings of the 11th International Conference on Concurrency Theory
Minimum-Cost Reachability for Priced Timed Automata
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Optimal Paths in Weighted Timed Automata
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
As Cheap as Possible: Efficient Cost-Optimal Reachability for Priced Timed Automata
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
Optimal scheduling using priced timed automata
ACM SIGMETRICS Performance Evaluation Review
On the optimal reachability problem of weighted timed automata
Formal Methods in System Design
Optimal reachability for multi-priced timed automata
Theoretical Computer Science
Optimal infinite scheduling for multi-priced timed automata
Formal Methods in System Design
Infinite Runs in Weighted Timed Automata with Energy Constraints
FORMATS '08 Proceedings of the 6th international conference on Formal Modeling and Analysis of Timed Systems
Weighted Timed Automata: Model-Checking and Games
Electronic Notes in Theoretical Computer Science (ENTCS)
Deciding an interval logic with accumulated durations
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
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We investigate the optimum reachability problem for Multi-Priced Timed Automata (MPTA) that admit both positive and negative costs on edges and locations, thus bridging the gap between the results of Bouyer et al. (2007) and of Larsen and Rasmussen (2008). Our contributions are the following: (1) We show that even the location reachability problem is undecidable for MPTA equipped with both positive and negative costs, provided the costs are subject to a bounded budget, in the sense that paths of the underlying Multi-Priced Transition System (MPTS) that operationally exceed the budget are considered as not being viable. This undecidability result follows from an encoding of Stop-Watch Automata using such MPTA, and applies to MPTA with as few as two cost variables, and even when no costs are incurred upon taking edges. (2) We then restrict the MPTA such that each viable quasi-cyclic path of the underlying MPTS incurs a minimum absolute cost. Under such a condition, the location reachability problem is shown to be decidable and the optimum cost is shown to be computable for MPTA with positive and negative costs and a bounded budget. These results follow from a reduction of the optimum reachability problem to the solution of a linear constraint system representing the path conditions over a finite number of viable paths of bounded length.