Topics in Region Theory and Synthesis Problems

Regions, as introduced by Ehrenfeucht and Rozenberg more than thirty years ago, have been used as a fundamental tool in synthesis problems, where a Petri net of a specific type must be built from a specification given in terms of a transition system. Some topics emerged in the research on regions are discussed, and a few open problems are stated. In particular, the paper focuses on three areas: (1) the notion of ‘type of nets’ as a tool for unifying the theory of regions, and as a notion leading to new variants of Petri nets; (2) the algebraic aspects of region theory; (3) the proposal of a new type of regions, inspired by reaction systems, and the potential for studying problems of synthesis of reaction systems.