Some Complexity Results for Rings of Petri Nets

Received (received date) Revised (revised date) Communicated by Editor's name ABSTRACT We deene a subclass of Petri nets called m?state n?cycle Petri nets, each of which can be thought of as a ring of n bounded (by m states) Petri nets using n potentially unbounded places as joins. Let Ring(n; l; m) be the class of m?state n?cycle Petri nets in which the largest integer mentioned can be represented in l bits (when the standard binary encoding scheme is used). As it turns out, both the reachability problem and the boundedness problem can be decided in O(n(l + log m)) nondeterministic space. Our results provide a slight improvement over previous results for the so-called cyclic communicating nite state machines. We also compare and contrast our results with that of V ASS(n;l; s), which represents the class of n-dimensional s-state VASSs where the largest integer mentioned can be described in l bits.