Timed-Arc Petri Nets vs. Networks of Timed Automata
Jir · 2005
We establish mutual translations between the classes of 1- safe timed-arc Petri nets (and its extension with testing arcs) and net- works of timed automata (and its subclass where every clock used in the guard has to be reset). The presented translations are very tight (up to isomorphism of labelled transition systems with time). This provides a convenient characterization from the theoretical point of view but is not always satisfactory from the practical point of view because of the possi- ble non-polynomial blow up in the size (in the direction from automata to nets). Hence we relax the isomorphism requirement and provide efficient (polynomial time) reductions between networks of timed automata and 1-safe timed-arc Petri nets preserving the answer to the reachability ques- tion. This makes our techniques suitable for automatic translation into a format required by tools like UPPAAL and KRONOS. A direct corol- lary of the presented reductions is a new PSPACE-completeness result for reachability in 1-safe timed-arc Petri nets, reusing the region/zone techniques already developed for timed automata.