  We investigate Petri nets with data, an extension of plain Petri nets where
tokens carry values from an infinite data domain, and executability of
transitions is conditioned by equalities between data values. We provide a
decision procedure for the bi-reachability problem: given a Petri net and its
two configurations, we ask if each of the configurations is reachable from the
other. This pushes forward the decidability borderline, as the bi-reachability
problem subsumes the coverability problem (which is known to be decidable) and
is subsumed by the reachability problem (whose decidability status is unknown).
