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.

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递归 Petri 网中的可覆盖性、终止性和有限性

早在 2000 年代，递归 Petri 网就被引入，以便对需要计数器和递归性的多代理系统的分布式规划进行建模。尽管递归 Petri 网严格扩展了 Petri 网和上下文无关文法，但已知大多数常见问题（可达性、可覆盖性、有限性、有界性和终止性）可以通过使用非原始递归算法来解决。对于几乎所有其他包含堆栈的扩展 Petri 网模型，可覆盖性和终止的复杂性未知或严格大于 EXPSPACE。相比之下，我们在这里确定，对于递归 Petri 网，可覆盖性、终止性、有界性和有限性问题与 Petri 网一样是 EXPSPACE 完全的。从表现力的角度来说，我们证明递归 Petri 网的可覆盖性语言严格包括 Petri 网的可覆盖性语言和上下文无关语言的联合。因此，我们免费获得了比 Petri 网更强大的模型。