Normal Petri Nets

Abstract A class of Petri nets, called normal Petri nets, is introduced, and it is shown that, for each initial marking, the reachability set of a normal marked Petri net is an effectively computable semilinear set. More generally, we show that the reachability set of a marked Petri net is an effectively computable semilinear set unless the total number of tokens in a minimal circuit is decreased to 0. We also show that a Petri net is normal if and only if it is weakly persistent for each initial marking without token-free circuits.