Decidable Classes of Unbounded Petri Nets with Time and Urgency

Sundararaman Akshay (1) , Blaise Genest (2) , Loïc Hélouët (2)

1 Department of Computer Science and Engineering [Bombay]
2 SUMO - SUpervision of large MOdular and distributed systems

Adding real time information to Petri net models often leads to un-decidability of classical verification problems such as reachability and bounded-ness. For instance, models such as Timed-Transition Petri nets (TPNs) are intractable except in a bounded setting. On the other hand, the model of Timed-Arc Petri nets enjoys decidability results for boundedness and control-state reachability problems at the cost of disallowing urgency (the ability to enforce actions within a time delay). Our goal is to investigate decidable classes of Petri nets with time that capture some urgency and still allow unbounded behaviors, which go beyond finite state systems. We present, up to our knowledge, the first decidability results on reachability and boundedness for Petri net variants that combine unbounded places, time, and urgency. For this, we introduce the class of Timed-Arc Petri nets with restricted Urgency, where urgency can be used only on transitions consuming tokens from bounded places. We show that control-state reachability and boundedness are de-cidable for this new class, by extending results from Timed-Arc Petri nets (without urgency). Our main result concerns (marking) reachability, which is un-decidable for both TPNs (because of unrestricted urgency) [20] and Timed-Arc Petri Nets (because of infinite number of " clocks "). We obtain decidability of reachability for unbounded TPNs with restricted urgency under a new, yet natural , timed-arc semantics presenting them as Timed-Arc Petri Nets with restricted urgency. Decidability of reachability under the intermediate marking semantics is also obtained for a restricted subclass.

Domaines: Théorie et langage formel [cs.FL]

Sundararaman Akshay, Blaise Genest, Loïc Hélouët. Decidable Classes of Unbounded Petri Nets with Time and Urgency. Application and Theory of Petri Nets and Concurrency - 37th International Conference, PETRI NETS, 2016, Torun University, Jun 2016, Torun, Poland. pp.301 - 322, ⟨10.1007/978-3-319-39086-4_18⟩. ⟨hal-01379414⟩