Abstract
The Petri net model is a powerful state transition oriented model to analyse, model and evaluate asynchronous and concurrent systems. However, like other state transition models, it encounters the state explosion problem. The size of the state space increases exponentially with the system complexity.
This paper is concerned with a method of abstracting automatically Petri nets to simpler representations, which are ordered with respect to their size. Thus it becomes possible to check Petri net reachability incrementally. With incremental approach we can overcome the exponential nature of Petri net reachability checking. We show that by using the incremental approach, the upper computational complexity bound for Petri net reachability checking with optimal abstraction hierarchies is polynomial.
The method we propose considers structural properties of a Petri net as well an initial and a final marking. In addition to Petri net abstraction irrelevant transitions for a given reachability problem are determined. By removing these transitions from a net, impact of the state explosion problem is reduced even more.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Anderson, J.S., Farley, A.M.: Plan abstraction based on operator generalization. In: Proceedings of the Seventh National Conference on Artificial Intelligence, Saint Paul, MN, pp. 100–104 (1988)
Berthelot, G.: Transformations and decompositions of nets. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 254, pp. 359–376. Springer, Heidelberg (1987)
Christensen, J.: Automatic Abstraction in Planning. PhD thesis, Department of Computer Science, Stanford University (1991)
Esparza, J., Nielsen, M.: Decidability issues for Petri nets—a survey. Journal of Information Processing and Cybernetics 30, 143–160 (1995)
Holte, R.C., Mkadmi, T., Zimmer, R.M., MacDonald, A.J.: Speeding up problem solving by abstraction: A graph oriented approach. Artificial Intelligence 85, 321–361 (1996)
Karp, R.M., Miller, R.E.: Parallel program schemata. Journal of Computer and Systems Sciences 3(2), 147–195 (1969)
Knoblock, C.A.: Automatically generating abstractions for planning. Artificial Intelligence 68, 243–302 (1994)
Korf, R.E.: Planning as search: A quantitative approach. Artificial Intelligence 33, 65–88 (1987)
Levy, A.Y.: Creating abstractions using relevance reasoning. In: Proceedings of the Twelfth National Conference on Artificial Intelligence (AAAI 1994), pp. 588–594 (1994)
Lipton, R.J.: The reachability problem requires exponential space. Research Report 62, Department of Computer Science, Yale University (1976)
Murata, T.: Petri nets: Properties, analysis and applications. Proceedings of IEEE 77(4), 541–580 (1989)
Newell, A., Simon, H.A.: Human Problem Solving. Prentice-Hall, Englewood Cliffs (1972)
Song, J.-S., Satoh, S., Ramamoorthy, C.V.: The abstraction of petri net. In: Proceedings of TENCON 1987, Seoul, Korea, August 25–28, pp. 467–471. IEEE Press, Los Alamitos (1987)
Suzuki, I., Murata, T.: A method for stepwise refinement and abstraction of petri nets. Journal of Computer and System Sciences 27, 51–76 (1983)
Vallette, R.: Analysis of petri nets by stepwise refinement. Journal of Computer and System Sciences 18(1), 35–46 (1979)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Küngas, P. (2005). Petri Net Reachability Checking Is Polynomial with Optimal Abstraction Hierarchies. In: Zucker, JD., Saitta, L. (eds) Abstraction, Reformulation and Approximation. SARA 2005. Lecture Notes in Computer Science(), vol 3607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11527862_11
Download citation
DOI: https://doi.org/10.1007/11527862_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27872-6
Online ISBN: 978-3-540-31882-8
eBook Packages: Computer ScienceComputer Science (R0)