Abstract
Petri nets are a successful formal method for the modeling and verification of asynchronous, concurrent and distributed systems. Reachability analysis can provide important information about the behavior of the model. However, reachability analysis is a computationally hard problem, especially when the state space is infinite. Abstraction-based techniques are often applied to overcome complexity. In this paper we analyze an algorithm, which uses counterexample guided abstraction refinement. This algorithm proved its efficiency on the model checking contest. We examine the algorithm from a theoretical and practical point of view. On the theoretical side, we show that the algorithm cannot decide reachability for relatively simple instances. We propose a new iteration strategy to explore the invariant space, which extends the set of decidable problems. We also give proofs on the theoretical limits of our approach. On the practical side, we examine different search strategies and we present our new, complex strategy with superior performance compared to traditional strategies. Measurements show that our new contributions perform well for traditional benchmark models as well.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Beyer, D., Henzinger, T., Jhala, R., Majumdar, R.: The software model checker Blast. International Journal on Software Tools for Technology Transfer 9(5–6), 505–525 (2007)
Ciardo, G., Lüttgen, G., Siminiceanu, R.: Saturation: an efficient iteration strategy for symbolic state-space generation. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 328–342. Springer, Heidelberg (2001)
Ciardo, G., Zhao, Y., Jin, X.: Ten years of saturation: a Petri net perspective. In: Jensen, K., Donatelli, S., Kleijn, J. (eds.) ToPNoC V. LNCS, vol. 6900, pp. 51–95. Springer, Heidelberg (2012)
Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement for symbolic model checking. J. ACM 50(5), 752–794 (2003)
Clarke, E.M., Grumberg, O., Long, D.E.: Model checking and abstraction. ACM Trans. Program. Lang. Syst. 16(5), 1512–1542 (1994)
Dantzig, G.B., Thapa, M.N.: Linear programming 1: introduction. Springer-Verlag New York Inc., Secaucus (1997)
Dijkstra, E.: Hierarchical ordering of sequential processes. Acta Informatica 1(2), 115–138 (1971)
Hajdu, Á., Vörös, A., Tamás, B., Mártonka, Z.: Extensions to the CEGAR approach on Petri nets. Acta Cybernetica 21(3), 401–417 (2014)
John, A., Konnov, I., Schmid, U., Veith, H., Widder, J.: Parameterized model checking of fault-tolerant distributed algorithms by abstraction. In: Formal Methods in Computer-Aided Design (FMCAD), pp. 201–209, October 2013
Kordon, F., Linard, A., Becutti, M., Buchs, D., Fronc, L., Hulin-Hubard, F., Legond-Aubry, F., Lohmann, N., Marechal, A., Paviot-Adet, E., Pommereau, F., Rodrígues, C., Rohr, C., Thierry-Mieg, Y., Wimmel, H., Wolf, K.: Web report on the model checking contest @ Petri net 2013, June 2013. http://mcc.lip6.fr
Lipton, R.: The Reachability Problem Requires Exponential Space. Research report, Yale University, Dept. of Computer Science (1976)
Mayr, E.W.: An algorithm for the general Petri net reachability problem. In: Proceedings of the Thirteenth Annual ACM Symposium on Theory of Computing, pp. 238–246. STOC 1981. ACM, New York (1981)
Murata, T.: Petri nets: Properties, analysis and applications. Proceedings of the IEEE 77(4), 541–580 (1989)
Vörös, A., Darvas, D., Bartha, T.: Bounded saturation based CTL model checking. In: Proceedings of the 12th Symposium on Programming Languages and Software Tools, SPLST 2011 (2011)
Website of PetriDotNet. http://inf.mit.bme.hu/en/research/tools/petridotnet (online accessed March 22, 2015)
Website of the models used in the measurements. http://inf.mit.bme.hu/en/pn2015 (online accessed March 22, 2015)
Website of the SARA tool. http://www.service-technology.org/sara/index.html (online accessed March 22, 2015)
Wimmel, H., Wolf, K.: Applying CEGAR to the Petri net state equation. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 224–238. Springer, Heidelberg (2011)
Wimmel, H., Wolf, K.: Applying CEGAR to the Petri net state equation. Logical Methods in Computer Science 8(3) (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Hajdu, Á., Vörös, A., Bartha, T. (2015). New Search Strategies for the Petri Net CEGAR Approach. In: Devillers, R., Valmari, A. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2015. Lecture Notes in Computer Science(), vol 9115. Springer, Cham. https://doi.org/10.1007/978-3-319-19488-2_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-19488-2_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19487-5
Online ISBN: 978-3-319-19488-2
eBook Packages: Computer ScienceComputer Science (R0)