Theory of regions

The Theory of regions is an approach for synthesizing a Petri net from a transition system. As such, it aims at recovering concurrent, independent behavior from transitions between global states. Theory of regions handles elementary net systems as well as P/T nets and other kinds of nets. An important point is that the approach is aimed at the synthesis of unlabeled Petri nets only.

Definition
A region of a transition system $$(S, \Lambda, \rightarrow)$$ is a mapping assigning to each state $$s \in S$$ a number $$\sigma(s)$$ (natural number for P/T nets, binary for ENS) and to each transition label a number $$\tau(\ell)$$ such that consistency conditions $$\sigma(s') = \sigma(s) + \tau(\ell)$$ holds whenever $$(s,\ell,s') \in \rightarrow$$.

Intuitive explanation
Each region represents a potential place of a Petri net.

Mukund: event/state separation property, state separation property.