  In a previous paper we introduced immediate observation Petri nets, a
subclass of Petri nets with application domains in distributed protocols
(population protocols) and theoretical chemistry (chemical reaction networks).
IO nets enjoy many useful properties, but like the general case of conservative
Petri nets they have a PSPACE-complete reachability problem. In this paper we
explore two restrictions of the reachability problem for IO nets which lower
the complexity of the problem drastically. The complexity is NP-complete for
the first restriction with applications in distributed protocols, and it is
polynomial for the second restriction with applications in chemical settings.
