On minimal representations of Petri net languages

Given a metric over the class of labeled Petri nets, we consider the existence of a procedure that takes as input a description of an arbitrary, labeled Petri net, and returns a description of a (possibly different) labeled Petri net with the smallest metric that generates the same language as the input. We refer to such procedures as minimization procedures. In this paper we investigate the existence of minimization procedures for a variety of metrics.