Complexity of Petri net reachability

Determine the exact computational complexity of the reachability problem for general place/transition Petri nets, i.e., deciding whether a given marking M is reachable from an initial marking M0 in a Petri net (N, M0).

Background

Reachability for Petri nets is known to be decidable (Mayr; Kosaraju; Lambert), yet its precise complexity classification has resisted resolution. Lipton established an EXPSPACE lower bound, while all known algorithms require non-primitive recursive space, leaving a large gap.

Numerous subclasses have tight complexity bounds (e.g., EXPSPACE-complete for symmetric nets, PSPACE-complete for 1-safe nets), but the general problem’s exact complexity remains unsettled.