Petri net theory has nice theorems which relate subclasses of Petri nets defined by structural conditions -- for example T-nets (also known as marked graphs) and free choice nets -- to their behavioural properties -- such as checking, given a net together with an initial marking, whether it exhibits a bounded amount of concurrency, or whether a transition can be fired, or whether a transition can be fired from any reachable marking. We argue that these theorems can be viewed as identifying nice communication patterns between different components of the given net (joint work with Madhavan Mukund and Ramchandra Phawade).
