Decidability of properties of timed-arc Petri nets

Abstract

Timed-arc Petri nets (TAPN’s) are not Turing powerful, because, in particular, they cannot simulate a counter with zero testing. Thus, we could think that this model does not increase significantly the expressiveness of untimed Petri nets. But this is not true; in a previous paper we have shown that the differences between them are big enough to make the reachability problem undecidable. On the other hand, coverability and boundedness are proved now to be decidable. This fact is a consequence of the close interrelationship between TAPN’s and transfer nets, for which similar results have been recently proved. Finally, we see that if dead tokens are defined as those that cannot be used for firing any transition in the future, we can detect these kind of tokens in an effective way.