  We introduce immediate observation Petri nets, a class of interest in the
study of population protocols (a model of distributed computation), and
enzymatic chemical networks. In these areas, relevant analysis questions
translate into parameterized Petri net problems: whether an infinite set of
Petri nets with the same underlying net, but different initial markings,
satisfy a given property. We study the parameterized reachability,
coverability, and liveness problems for immediate observation Petri nets. We
show that all three problems are in PSPACE for infinite sets of initial
markings defined by counting constraints, a class sufficiently rich for the
intended application. This is remarkable, since the problems are already
PSPACE-hard when the set of markings is a singleton, i.e., in the
non-parameterized case. We use these results to prove that the correctness
problem for immediate observation population protocols is PSPACE-complete,
answering a question left open in a previous paper.
