Improving Saturation Efficiency with Implicit Relations
- 321 Downloads
Decision diagrams are a well-established data structure for reachability set generation and model checking of high-level models such as Petri nets, due to their versatility and the availability of efficient algorithms for their construction. Using a decision diagram to represent the transition relation of each event of the high-level model, the saturation algorithm can be used to construct a decision diagram representing all states reachable from an initial set of states, via the occurrence of zero or more events. A difficulty arises in practice for models whose state variable bounds are unknown, as the transition relations cannot be constructed before the bounds are known. Previously, on-the-fly approaches have constructed the transition relations along with the reachability set during the saturation procedure. This can affect performance, as the transition relation decision diagrams must be rebuilt, and compute-table entries may need to be discarded, as the size of each state variable increases. In this paper, we introduce a different approach based on an implicit and unchanging representation for the transition relations, thereby avoiding the need to reconstruct the transition relations and discard compute-table entries. We modify the saturation algorithm to use this new representation, and demonstrate its effectiveness with experiments on several benchmark models.
KeywordsPetri nets Decision diagram Saturation Reachability set generation
This work was supported in part by the National Science Foundation under grant ACI-1642397.
- 1.MCC: Model Checking Competition @ Petri Nets. https://mcc.lip6.fr
- 2.MEDDLY webpage. https://sourceforge.net/projects/meddly/
- 3.Babar, J., Miner, A.S.: Meddly: multi-terminal and Edge-valued Decision Diagram LibrarY. In: Proceedings of QEST, pp. 195–196. IEEE Computer Society (2010)Google Scholar
- 9.Ciardo, G., Miner, A.S.: SMART: simulation and Markovian analyzer for reliability and timing. In: Proceedings of IEEE International Computer Performance and Dependability Symposium (IPDS 1996), p. 60. IEEE Computer Society Press (1996)Google Scholar
- 11.Couvreur, J.-M., Encrenaz, E., Paviot-Adet, E., Poitrenaud, D., Wacrenier, P.-A.: Data decision diagrams for Petri net analysis. In: Esparza, J., Lakos, C. (eds.) ICATPN 2002. LNCS, vol. 2360, pp. 101–120. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-48068-4_8CrossRefzbMATHGoogle Scholar
- 15.Miner, A.S.: Saturation for a general class of models. In: Proceedings of QEST, pp. 282–291, September 2004Google Scholar
- 17.Strehl, K., Thiele, L.: Interval diagram techniques for symbolic model checking of Petri nets. In: Proceedings of Design, Automation and Test in Europe (DATE 1999), pp. 756–757, March 1999Google Scholar
- 19.Wan, M., Ciardo, G.: Symbolic state-space generation of asynchronous systems using extensible decision diagrams. In: Nielsen, M., Kučera, A., Miltersen, P.B., Palamidessi, C., Tůma, P., Valencia, F. (eds.) SOFSEM 2009. LNCS, vol. 5404, pp. 582–594. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-540-95891-8_52CrossRefzbMATHGoogle Scholar