Abstract
As a means to tackle the state explosion problem of model checking 1-safe Petri nets for linear time logic without next-time (LTL\(_{\textrm{-\tiny{X}}}\)), an approach that combines compositional verification and Petri net reductions is presented. We decompose a Petri net into (i) a so-called kernel net Σ k containing all places mentioned by the LTL\(_{\textrm{-\tiny{X}}}\) property φ and (ii) environment subnets . These environment nets do not interact with each other and have limited influence on the kernel only. Six distinct and very simple summary nets suffice to describe the influence of any environment net. To determine the appropriate summary net we modularly verify up to three fixed LTL\(_{\textrm{-\tiny{X}}}\) formulas on . We reduce Σ by replacing every environment subnet in Σ by its summary net. Instead of checking φ on Σ, we check φ on the reduced net. Verification of several case-studies shows that our reduction approach can significantly speed-up model checking.
This work is supported by the German Research Foundation (DFG), grant GRK 1076/1.
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
Lee, W.J., Cha, S.D., Kwon, Y.R., Kim, H.N.: A Slicing-based Approach to Enhance Petri Net Reachability Analysis. Journal of Research and Practice in Information Technology 3, 131–143 (2000)
Klai, K., Petrucci, L., Reniers, M.: An Incremental and Modular Technique for Checking LTL∖X Properties of Petri nets. In: Derrick, J., Vain, J. (eds.) FORTE 2007. LNCS, vol. 4574, pp. 280–295. Springer, Heidelberg (2007)
Valmari, A.: Compositional Analysis with Place-Bordered Subnets. In: Valette, R. (ed.) ICATPN 1994. LNCS, vol. 815, pp. 531–547. Springer, Heidelberg (1994)
Berthelot, G.: Checking Properties of Nets Using Transformation. In: Rozenberg, G. (ed.) APN 1985. LNCS, vol. 222, pp. 19–40. Springer, Heidelberg (1986)
Desel, J., Esparza, J.: Free choice Petri Nets. Cambridge University Press, New York (1995)
Poitrenaud, D., Pradat-Peyre, J.-F.: Pre- and Post-agglomerations for LTL Model Checking. In: Nielsen, M., Simpson, D. (eds.) ICATPN 2000. LNCS, vol. 1825, pp. 387–408. Springer, Heidelberg (2000)
Esparza, J., Schröter, C.: Net Reductions for LTL Model-Checking. In: Margaria, T., Melham, T.F. (eds.) CHARME 2001. LNCS, vol. 2144, pp. 310–324. Springer, Heidelberg (2001)
Haddad, S., Pradat-Peyre, J.-F.: New Efficient Petri Nets Reductions for Parallel Programs Verification. In: Parallel Processing Letters, vol. 16(1), pp. 101–116. World Scientific Publishing Company, Singapore (2006)
Valmari, A.: On-the-Fly Verification with Stubborn Sets. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 397–408. Springer, Heidelberg (1993)
Lamport, L.: What Good is Temporal Logic? In: Information Processing 1983: Proceedings of the IFIO 9th World Computer Congress, pp. 657–668 (1983)
Rakow, A.: Decompositional Petri Net Reductions. Technical Report (June 2008), http://parsys.informatik.uni-oldenburg.de/~astrid3/ifm/reducts.pdf
Rakow, A.: Slicing Petri nets with an Application to Workflow Verification. In: Geffert, V., Karhumäki, J., Bertoni, A., Preneel, B., Návrat, P., Bieliková, M. (eds.) SOFSEM 2008. LNCS, vol. 4910, pp. 436–447. Springer, Heidelberg (2008)
http://sparcs.kaist.ac.kr/~lacrimosa/algorithm/2003/CS300-09.ppt
Diestel, R.: Graph Theory. Graduate Texts in Mathematics, vol. 173. Springer, Heidelberg (2005)
Cheng, A., Esparza, J., Palsberg, J.: Complexity Results for 1-safe nets. In: Shyamasundar, R.K. (ed.) FSTTCS 1993. LNCS, vol. 761, pp. 326–337. Springer, Heidelberg (1993)
Girault, C., Valk, R.: Petri Nets for System Engineering: A Guide to Modeling, Verification, and Applications. Springer, New York (2001)
Corbett, J.C.: Evaluating Deadlock Detection Methods for Concurrent Software. IEEE Transactions on Software Engineering 22(3), 161–180 (1996)
http://parsys.informatik.uni-oldenburg.de/~astrid3/ifm/bm.tar.gz
Esparza, J., Heljanko, K.: Implementing LTL Model Checking with Net Unfoldings. Research Report A68, Laboratory for Theoretical Computer Science, Helsinki University of Technology, Espoo, Finland, 29p. (March 2001)
Schröter, C., Khomenko, V.: Parallel LTL-X Model Checking of High-Level Petri Nets Based on Unfoldings. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 109–121. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rakow, A. (2009). Decompositional Petri Net Reductions. In: Leuschel, M., Wehrheim, H. (eds) Integrated Formal Methods. IFM 2009. Lecture Notes in Computer Science, vol 5423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00255-7_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-00255-7_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00254-0
Online ISBN: 978-3-642-00255-7
eBook Packages: Computer ScienceComputer Science (R0)