Expand, Enlarge and Check... Made Efficient
The coverability problem is decidable for the class of well-structured transition systems. Until recently, the only known algorithm to solve this problem was based on symbolic backward reachability. In a recent paper, we have introduced the theory underlying a new algorithmic solution, called ‘Expand, Enlarge and Check’, which can be implemented in a forward manner. In this paper, we provide additional concepts and algorithms to turn this theory into efficient forward algorithms for monotonic extensions of Petri nets and Lossy Channels Systems. We have implemented a prototype and applied it on a large set of examples. This prototype outperforms a previous fine tuned prototype based on backward symbolic exploration and shows the practical interest of our new algorithmic solution.
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- 1.Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.-K.: General Decidability Theorems for Infinite-state Systems. In: Proc. of LICS 1996, pp. 313–321. IEEE, Los Alamitos (1996)Google Scholar
- 4.Ciardo, G.: Petri nets with marking-dependent arc multiplicity: properties and analysis. In: Valette, R. (ed.) ICATPN 1994. LNCS, vol. 815, pp. 179–198. Springer, Heidelberg (1994)Google Scholar
- 6.Emerson, E.A., Namjoshi, K.S.: On Model Checking for Non-deterministic Infinite-state Systems. In: Proc. of LICS 1998, pp. 70–80. IEEE, Los Alamitos (1998)Google Scholar
- 7.Esparza, J., Finkel, A., Mayr, R.: On the Verification of Broadcast Protocols. In: Proc. of LICS 1999, pp. 352–359. IEEE, Los Alamitos (1999)Google Scholar
- 8.Finkel, A.: The minimal coverability graph for Petri nets. In: Rozenberg, G. (ed.) APN 1993. LNCS, vol. 674, pp. 210–243. Springer, Heidelberg (1993)Google Scholar
- 10.Finkel, A., Geeraerts, G., Raskin, J.-F., Van Begin, L.: A counter-example to the minimal coverability tree algorithm, Technical report ULB 535, http://www.ulb.ac.be/di/ssd/ggeeraer/papers/FGRV05-Coverability.pdf
- 14.Van Begin, L.: Efficient Verification of Counting Abstractions for Parametric systems. PhD thesis, Université Libre de Bruxelles, Belgium (2003)Google Scholar