Analyzing Reachability for Some Petri Nets With Fast Growing Markings

Using linear algebraic techniques, we analyse the computational complexity of testing reachability in Petri nets for which markings can grow very fast. This leads to two subclasses of Petri nets for which the reachability problem is PSPACE-complete. These subclasses are not contained in any other subclass for which complexity of the reachability problem was known, such as those given in Esparza and Nielsen's survey [Esparza, J. and M. Nielsen, Decidability issues for Petri nets — a survey, J. Inform. Process. Cybernet. 30 (1994), pp. 143–160]. We give an example where further extension of our subclasses fails to maintain the upper bound.