On Nonlinear Prices in Timed Automata
For researchers in real-time systems and verification, this work establishes fundamental limits of decidability for nonlinear pricing, though the implementation is preliminary.
The paper investigates priced timed automata with nonlinear prices, proving that the optimal reachability problem becomes undecidable in the most general setting. It adapts a previous construction using the Z3 theorem prover and presents preliminary results.
Priced timed automata provide a natural model for quantitative analysis of real-time systems and have been successfully applied in various scheduling and planning problems. The optimal reachability problem for linearly-priced timed automata is known to be PSPACE-complete. In this paper we investigate priced timed automata with more general prices and show that in the most general setting the optimal reachability problem is undecidable. We adapt and implement the construction of Audemard, Cimatti, Kornilowicz, and Sebastiani for non-linear priced timed automata using state-of-the-art theorem prover Z3 and present some preliminary results.