We develop a polynomial translation from finite control pi-calculus processes to safe low-level Petri nets. To our knowledge, this is the first such translation. It is natural in that there is a close correspondence between the control flows, enjoys a bisimulation result, and is suitable for practical model checking.
We study the decidability of the control reachability problem for various fragments of the asynchronous π-calculus. We consider the combination of three main features: name generation, name mobility, and unbounded control. We show that the combination of name generation with either name mobility or unbounded control leads to an undecidable fragment. On the other hand, we prove that name generation with unique receiver and bounded input (a condition weaker than bounded control) is decidable by reduction to the coverability problem for Petri nets with transfer (and back). We study Petri nets with Reset arcs (also Transfer and Doubling arcs) in combination with other extensions of the basic Petri net model. While Reachability is undecidable in all these extensions (indeed they are Turing-powerful), we exhibit unexpected frontiers for the decidability of Termination, Coverability, Boundedness and place-Boundedness. In particular, we show counter-intuitive separations between seemingly related problems. Our main theorem is the very surprising fact that boundedness is undecidable for Petri nets with Reset arcs.