In the early two-thousands, Recursive Petri nets have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. Although Recursive Petri nets strictly extend Petri nets and contex
t-free grammars, most of the usual problems (reachability, coverability, finiteness, boundedness and termination) were known to be solvable by using non-primitive recursive algorithms. For almost all other extended Petri nets models containing a stack, the complexity of coverability and termination are unknown or strictly larger than EXPSPACE. In contrast, we establish here that for Recursive Petri nets, the coverability, termination, boundedness and finiteness problems are EXPSPACE-complete as for Petri nets. From an expressiveness point of view, we show that coverability languages of Recursive Petri nets strictly include the union of coverability languages of Petri nets and context-free languages. Thus we get a more powerful model than Petri net for free.
Location-Based Services (LBSs) provide invaluable aid in the everyday activities of many individuals, however they also pose serious threats to the user privacy. There is, therefore, a growing interest in the development of mechanisms to protect loca
tion privacy during the use of LBSs. Nowadays, the most popular methods are probabilistic, and the so-called optimal method achieves an optimal trade-off between privacy and utility by using linear optimization techniques. Unfortunately, due to the complexity of linear programming, the method is unfeasible for a large number n of locations, because the constraints are $O(n^3)$. In this paper, we propose a technique to reduce the number of constraints to $O(n^2)$, at the price of renouncing to perfect optimality. We show however that on practical situations the utility loss is quite acceptable, while the gain in performance is significant.
