Zone extrapolations in parametric timed automata

Timed automata (TAs) are an efficient formalism to model and verify systems with hard timing constraints and concurrency. While TAs assume exact timing constants with infinite precision, parametric timed automata (PTAs) overcome this limitation and increase their expressiveness—at the cost of undecidability of most interesting problems. A practical explanation for the efficiency of nonparametric TAs is zone extrapolation, where clock valuations beyond a given constant are considered equivalent. This concept cannot be easily extended to PTAs, due to the fact that parameters can be unbounded, meaning that the constants compared to the clocks have no upper bound. In this work, we propose several definitions of extrapolation for PTAs, and we study their correctness. Our experiments show an overall decrease of the computation time and, most importantly, allow termination of some previously unsolvable benchmarks.