  We introduce {\omega}-Petri nets ({\omega}PN), an extension of plain Petri
nets with {\omega}-labeled input and output arcs, that is well-suited to
analyse parametric concurrent systems with dynamic thread creation. Most
techniques (such as the Karp and Miller tree or the Rackoff technique) that
have been proposed in the setting of plain Petri nets do not apply directly to
{\omega}PN because {\omega}PN define transition systems that have infinite
branching. This motivates a thorough analysis of the computational aspects of
{\omega}PN. We show that an {\omega}PN can be turned into an plain Petri net
that allows to recover the reachability set of the {\omega}PN, but that does
not preserve termination. This yields complexity bounds for the reachability,
(place) boundedness and coverability problems on {\omega}PN. We provide a
practical algorithm to compute a coverability set of the {\omega}PN and to
decide termination by adapting the classical Karp and Miller tree construction.
We also adapt the Rackoff technique to {\omega}PN, to obtain the exact
complexity of the termination problem. Finally, we consider the extension of
{\omega}PN with reset and transfer arcs, and show how this extension impacts
the decidability and complexity of the aforementioned problems.
