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 context-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.
翻译:在最初的两千人中,为了模拟需要反转和复现的多试剂系统的分布式规划,引进了Recurive Petri 蚊帐,以模拟对需要反转和复现的多试剂系统的分布式规划;虽然再curvesive Petri 蚊帐严格扩展了Petri 蚊帐和无上下文的语法,但大多数常见问题(可及性、可复现性、有限性、约束性和终止性)已知可以通过使用非被动递转算法来溶解;对于几乎所有其他含有堆叠的扩展的Petri 蚊帐模型来说,可复现性和终止性的复杂性并不为人知,或严格大于EXPSPACE。相比之下,我们在此确定,对于再cursive Petri 蚊帐,可复现性、终止性、约束性和有限性问题是EXPSPACE与Petri 蚊帐一样完整的。我们从明确的角度表明,Recurissive Petri 蚊帐的可隐性语言严格包括可隐性语言和无上下文语言的结合。因此,我们得到了比Petri 网络更强大的免费的模型。