Abstract
The unconstrained step semantics of Petri nets is impractical for simulating and modelling applications. In the past, this inadequacy has been alleviated by introducing various flavours of maximally concurrent semantics, as well as priority orders. In this paper, we introduce a general way of controlling step semantics of Petri nets through step firing policies that restrict the concurrent behaviour of Petri nets and so improve their execution and modelling features. In a nutshell, a step firing policy disables at each marking a subset of enabled steps which could otherwise be executed. We discuss various examples of step firing policies and then investigate the synthesis problem for Petri nets controlled by such policies. Using generalised regions of step transition systems, we provide an axiomatic characterisation of those transition systems which can be realised as reachability graphs of Petri nets controlled by a given step firing policy. We also provide a decision and synthesis algorithm for PT-nets and step firing policies based on linear rewards of steps, where fixing the reward of elementary transitions is part of the synthesis problem. The simplicity of the algorithm supports our claim that the proposed approach is practical.
This is a preview of subscription content, log in via an institution to check access.
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
Badouel, E., Bernardinello, L., Darondeau, Ph.: Polynomial Algorithms for the Synthesis of Bounded Nets. In: Mosses, P.D., Nielsen, M., Schwartzbach, M.I. (eds.) TAPSOFT 1995. LNCS, vol. 915, pp. 364–378. Springer, Heidelberg (1995)
Badouel, E., Darondeau, P.: On the Synthesis of General Petri Nets. Report INRIA-RR 3025 (1996)
Badouel, E., Darondeau, P.: Theory of Regions. In: Reisig, W., Rozenberg, G. (eds.) Lectures on Petri Nets I: Basic Models. LNCS, vol. 1491, pp. 529–586. Springer, Heidelberg (1998)
Bernardinello, L., De Michelis, G., Petruni, K., Vigna, S.: On the Synchronic Structure of Transition Systems. In: Desel, J. (ed.) Structures in Concurrency Theory, pp. 11–31. Springer, Heidelberg (1996)
Busi, N., Pinna, G.M.: Synthesis of Nets with Inhibitor Arcs. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 151–165. Springer, Heidelberg (1997)
Chernikova, N.: Algorithm for Finding a General Formula for the Non-negative Solutions of a System of Linear Inequalities. USSR Computational Mathematics and Mathematical Physics 5, 228–233 (1965)
Cortadella, J., Kishinevsky, M., Kondratyev, A., Lavagno, L., Yakovlev, A.: Petrify: a tool for manipulating concurrent specifications and synthesis of asynchronous controllers. IEICE Trans. on Information and Systems E80-D, 315–325 (1997)
Darondeau, Ph., Koutny, M., Pietkiewicz-Koutny, M., Yakovlev, A.: Synthesis of Nets with Step Firing Policies. Report CS-TR-1080, Newcastle University (2008)
Desel, J., Reisig, W.: The Synthesis Problem of Petri Nets. Acta Informatica 33, 297–315 (1996)
Ehrenfeucht, A., Rozenberg, G.: Partial (Set) 2-Structures; Part I: Basic Notions and the Representation Problem. Acta Informatica 27, 315–342 (1990)
Ehrenfeucht, A., Rozenberg, G.: Partial (Set) 2-Structures; Part II: State Spaces of Concurrent Systems. Acta Informatica 27, 343–368 (1990)
Kleijn, J., Koutny, M., Rozenberg, G.: Towards a Petri Net Semantics for Membrane Systems. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2005. LNCS, vol. 3850, pp. 292–309. Springer, Heidelberg (2006)
Koutny, M., Pietkiewicz-Koutny, M.: Transition Systems of Elementary Net Systems with Localities. In: Baier, C., Hermanns, H. (eds.) CONCUR 2006. LNCS, vol. 4137, pp. 173–187. Springer, Heidelberg (2006)
Koutny, M., Pietkiewicz-Koutny, M.: Synthesis of Elementary Net Systems with Context Arcs and Localities. In: Kleijn, J., Yakovlev, A. (eds.) ICATPN 2007. LNCS, vol. 4546, pp. 281–300. Springer, Heidelberg (2007)
Mazurkiewicz, A.: Petri Nets Without Tokens. In: Kleijn, J., Yakovlev, A. (eds.) ICATPN 2007. LNCS, vol. 4546, pp. 20–23. Springer, Heidelberg (2007)
Mukund, M.: Petri Nets and Step Transition Systems. International Journal of Foundations of Computer Science 3, 443–478 (1992)
Pietkiewicz-Koutny, M.: The Synthesis Problem for Elementary Nets with Inhibitor Arcs. Fundamenta Informaticae 40, 251–283 (1999)
Schrijver, A.: Theory of Linear and Integer Programming. John Wiley, Chichester (1986)
Starke, P.: Some Properties of Timed Nets under the Earliest Firing Rule. In: Rozenberg, G. (ed.) APN 1989. LNCS, vol. 424, pp. 418–432. Springer, Heidelberg (1990)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Darondeau, P., Koutny, M., Pietkiewicz-Koutny, M., Yakovlev, A. (2008). Synthesis of Nets with Step Firing Policies. In: van Hee, K.M., Valk, R. (eds) Applications and Theory of Petri Nets. PETRI NETS 2008. Lecture Notes in Computer Science, vol 5062. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68746-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-68746-7_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68745-0
Online ISBN: 978-3-540-68746-7
eBook Packages: Computer ScienceComputer Science (R0)