Completeness Results for Generalized Communication-Free Petri Nets with Arbitrary Edge Multiplicities

Abstract

We investigate gcf-Petri nets, a generalization of communication-free Petri nets allowing arbitrary edge multiplicities, and characterized by the sole restriction that each transition has at most one incoming edge. We use canonical ring sequences with nice properties for gcf-PNs to show that the RecLFS, (zero-)reachability, covering, and boundedness problems of gcf-PNs are in PSPACE. By showing, how PSPACE-Turing machines can be simulated by gss-PNs, a subclass of gcf-PNs where additionally all transitions have at most one outgoing edge, we ultimately prove the PSPACE-completess of these problems for gss/gcf-PNs. Then, we show PSPACE-hardness as well as a doubly exponential space bound for the containment, and equivalence problems of gss/gcf-PNs. Last, we consider a new natural generalization of context-free commutative grammars. Our results for gcf-PNs imply PSPACE-completeness for its uniform word problem.