What a structural world [structural decomposition]

Petri nets and stochastic Petri nets have been widely adopted as one of the best tools to model the logical and timing behavior of discrete-state systems. However, their practical applicability is limited by the state-space explosion problem. We survey some of the techniques that have been used to cope with large state spaces, starting from early explicit methods, which require data structures of size proportional to the number of states or state-to-state transitions, then moving to implicit methods, which borrow ideas from symbolic model checking (binary decision diagrams) and numerical linear algebra (Kronecker operators) to drastically reduce the computational requirements. Next, we describe the structural decomposition approach which has been the topic of our research in the last few years. This method only requires to specify a partition of the places in the net and, combining decision diagrams and Kronecker operators with the new concepts of event locality and node saturation, achieves fundamental gains in both memory and time efficiency. At the same, the approach is applicable to a wide range of models. We conclude by considering several research directions that could further push the range of solvable models, eventually leading to an even greater industrial acceptance of this simple yet powerful modeling formalism