A Representation Theorem for Primitive Recursive Algorithms

2011 ◽  
Vol 107 (4) ◽  
pp. 313-330 ◽  
Author(s):  
Philippe Andary ◽  
Bruno Patrou ◽  
Pierre Valarcher
Keyword(s):  
Representation Theorem ◽  
Recursive Algorithms ◽  
Primitive Recursive

scholarly journals Coverability, Termination, and Finiteness in Recursive Petri Nets

2022 ◽  
Vol 183 (1-2) ◽  
pp. 33-66
Author(s):  
Alain Finkel ◽  
Serge Haddad ◽  
Igor Khmelnitsky
Keyword(s):  
Petri Nets ◽  
Point Of View ◽  
Recursive Algorithms ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Extended Petri Nets ◽  
Multi Agent ◽  
Almost All ◽  
Primitive Recursive ◽  
Context Free

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.

Sign in / Sign up

Export Citation Format

Share Document