We propose a framework for the specification of behaviourpreserving reconfigurations of systems modelled as Petri nets. The framework is based on open nets, a mild generalisation of ordinary Place/Transition nets suited to model open systems which might interact with the surrounding environment and endowed with a colimitbased composition operation. We show that natural notions of (strong and weak) bisimilarity over open nets are congruences with respect to the composition operation. We also provide an up-to technique for facilitating bisimilarity proofs. The theory is used to identify suitable classes of reconfiguration rules (in the double-pushout approach to rewriting) whose application preserves the observational semantics of the net.

Abstract. The paper introduces the notion of concurrent realization of reactive systems. A framework is also presented in which labelled safe Petri nets as concurrent realizations of concrete asynchronous systems are constructed. The construction is uniform in the sense that it extends to a realization of an arbitrary diagram. We discuss applicability of the framework to construct maximally concurrent realizations of reactive systems. 1

. The problem of finite completeness of categories of Petri nets is studied. Since Petri nets have finite products, the problem reduces to the issue of the existence of equalizers. We show that the categories of Petri nets with general and Winskel morphisms do not admit equalizers, and hence are not finitely complete. The main positive result of the paper states that reachable Petri nets with multiplicative morphisms form a finitely complete category. As an application of this result, some wellknown categories are shown to be finitely complete. For instance, since all morphisms between reachable safe Petri nets are multiplicative, it follows that the category of reachable safe Petri nets is finitely complete. Keywords: Categories of Petri nets, products, equalizers, (finite) completeness. 1. Introduction Studies of category-theoretical foundations of concurrent processes and their models go back to the work of Winskel in the 80s, see [15] for an account of the work done in this area....