Timed Petri Nets and Timed Automata: On the Discriminating Power of Zeno Sequences

Abstract

Abstract. Timed Petri nets and timed automata are two standard models for the analysis of real-time systems. In this paper, we prove that they are incomparable for the timed language equivalence. Thus we propose an extension of timed Petri nets with read-arcs (RA-TdPN), whose coverability problem is decidable. We also show that this model unifies timed Petri nets and timed automata. Then, we establish numerous expressiveness results and prove that zeno behaviours discriminate between several sub-classes of RA-TdPNs. This has surprising consequences on timed automata, for instance on the power of non-deterministic clock resets.

A Framework for Relating Timed Transition Systems and Preserving TCTL Model Checking

“…To this end, several translations have been developed (see e.g. [5,6,8,9,10,11,13,16] or [15,18] for a more complete overview) and some of them have been implemented in verification tools like Romeo [12], TAPAAL [9] or the TIOA Toolkit [2].…”

Comparing the Expressiveness of Timed Automata and Timed Extensions of Petri Nets

“…In some applications this might be undesirable and hence in [84] the model was extended with so-called read-arcs, which allow to test for a presence of a token in a certain place but do not change its age. It was later shown in [30] that this extension is not only convenient from the modelling point of view but it also extends the expressiveness of the model.…”

“…On the other hand, coverability, boundedness and other problems remain decidable for TAPN [77,3,1], which are also known to offer 'weak' expressiveness, in the sense that TAPN cannot simulate Turing machines [25]. Coverability is decidable even for TAPN extended with read-arcs [30]. These results hold due to the monotonicity property (adding more tokens to the net does not restrict the possible executions) and the application of well-quasi-ordering (for a general introduction see [48]) resp.…”

“…When we are interested only in the reachability questions, the reductions work in polynomial time. Recently Bouyer et al in [30] presented a reduction from bounded TAPN (with read-arcs) to 1-safe TAPN (with read-arcs) which preserves timed language equivalence (over finite words, infinite words and non-Zeno infinite words). This demonstrates that NTA without invariants and bounded TAPN with read-arcs are timed language equivalent.…”

“…This demonstrates that NTA without invariants and bounded TAPN with read-arcs are timed language equivalent. The authors in [30] also provide a number of expressiveness results for several subclasses of TAPN with read-arcs.…”