Abstract
Reconfigurable place/transition systems are Petri nets with initial markings and a set of rules which allow the modification of the net during runtime in order to adapt the net to new requirements of the environment. In this paper we use transformation rules for place/transition systems in the sense of the double pushout approach for graph transformation. The main problem in this context is to analyze under which conditions net transformations and token firing can be executed in arbitrary order. This problem is solved in the main theorems of this paper. Reconfigurable place/transition systems then are applied in a mobile network scenario.
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
Balbo, G., Bruell, S., Sereno, M.: Product Form Solution for Generalized Stochastic Petri Nets. IEEE Transactions on Software Engineering 28(10), 915–932 (2002)
Belli, F., Dreyer, J.: Systems Modelling and Simulation by Means of Predicate/Transition Nets and Logic Programming. In: IEA/AIE. Proc. Industrial and Engineering Applications of Artificial Intelligence and Expert Systems, pp. 465–474 (1994)
Berthelot, G.: Checking properties of nets using transformation. In: Rozenberg, G. (ed.) Advances in Petri Nets 1985. LNCS, vol. 222, pp. 19–40. Springer, Heidelberg (1986)
Berthelot, G.: Transformations and Decompositions of Nets. In: Petri Nets: Central Models and Their Properties, Part I, Advances in Petri Nets. LNCS, vol. 254, pp. 359–376. Springer, Heidelberg (1987)
Bessey, T., Becker, M.: Comparison of the modeling power of fluid stochastic Petri nets (FSPN) and hybrid Petri nets (HPN). In: Proc.Systems, Man and Cybernetics (SMC), vol. 2, pp. 354–358. IEEE Computer Society Press, Los Alamitos (2002)
Best, E., Thielke, T.: Orthogonal Transformations for Coloured Petri Nets. In: Azéma, P., Balbo, G. (eds.) ICATPN 1997. LNCS, vol. 1248, pp. 447–466. Springer, Heidelberg (1997)
Billington, J.: Extensions to Coloured Petri Nets. In: PNPM. Proc. Petri Nets and Performance Models, pp. 61–70. IEEE Computer Society Press, Los Alamitos (1989)
Bonhomme, P., Aygalinc, P., Berthelot, G., Calvez, S.: Hierarchical control of time Petri nets by means of transformations. In: SMC. Proc. Systems, Man and Cybernetics, vol. 4, p. 6. IEEE Computer Society Press, Los Alamitos (2002)
Bottoni, P., De Rosa, F., Hoffmann, K., Mecella, M.: Applying Algebraic Approaches for Modeling Workflows and their Transformations in Mobile Networks. Journal of Mobile Information Systems 2(1), 51–76 (2006)
Campos, J., Sánchez, B., Silva, M.: Throughput Lower Bounds for Markovian Petri Nets: Transformation Techniques. In: PNPM. Proc. Petri Nets and Performance Models, pp. 322–331. IEEE Computer Society Press, Los Alamitos (1991)
Carmona, J., Cortadella, J.: Input/Output Compatibility of Reactive Systems. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, pp. 360–377. Springer, Heidelberg (2002)
Chehaibar, G.: Replacement of Open Interface Subnets and Stable State Transformation Equivalence. In: Proc. Applications and Theory of Petri Nets (ATPN). LNCS, vol. 674, pp. 1–25. Springer, Heidelberg (1991)
Cheung, T., Lu, Y.: Five Classes of Invariant-Preserving Transformations on Colored Petri Nets. In: Donatelli, S., Kleijn, J.H.C.M. (eds.) ICATPN 1999. LNCS, vol. 1639, pp. 384–403. Springer, Heidelberg (1999)
Cortés, L., Eles, P., Peng, Z.: Modeling and formal verification of embedded systems based on a Petri net representation. Journal of Systems Architecture 49(12-15), 571–598 (2003)
de Lara, J., Vangheluwe, H.: Computer Aided Multi-Paradigm Modelling to Process Petri-Nets and Statecharts. In: Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2002. LNCS, vol. 2505, pp. 239–253. Springer, Heidelberg (2002)
Desel, J.: On Abstraction of Nets. In: Proc. Applications and Theory of Petri Nets (ATPN). LNCS, vol. 524, pp. 78–92. Springer, Heidelberg (1990)
Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. In: EATCS Monographs in Theoretical Computer Science, Springer, Heidelberg (2006)
Ehrig, H., Hoffmann, K., Prange, U., Padberg, J.: Formal Foundation for the Reconfiguaration of Nets. Technical report, TU Berlin, Fak. IV (2007)
Esparza, J.: Model Checking Using Net Unfoldings. Science of Computer Programming 23(2-3), 151–195 (1994)
Esparza, J., Silva, M.: On the analysis and synthesis of free choice systems. In: ATPN. LNCS, vol. 483, pp. 243–286. Springer, Heidelberg (1989)
Farwer, B., Köhler, M.: Mobile Object-Net Systems and their Processes. Fundamenta Informaticae 60(1-4), 113–129 (2004)
Haddad, S.: A Reduction Theory for Coloured Nets. In: ATPN. LNCS, vol. 424, pp. 209–235. Springer, Heidelberg (1988)
Hoffmann, K., Ehrig, H., Mossakowski, T.: High-Level Nets with Nets and Rules as Tokens. In: Ciardo, G., Darondeau, P. (eds.) ICATPN 2005. LNCS, vol. 3536, pp. 268–288. Springer, Heidelberg (2005)
Kindler, E., Weber, M.: The Petri Net Kernel - An Infrastructure for Building Petri Net Tools. Software Tools for Technology Transfer 3(4), 486–497 (2001)
Kluge, O.: Modelling a Railway Crossing with Message Sequence Charts and Petri Nets. In: Ehrig, H., Reisig, W., Rozenberg, G., Weber, H. (eds.) Petri Net Technology for Communication-Based Systems. LNCS, vol. 2472, pp. 197–218. Springer, Heidelberg (2003)
Köhler, M., Rölke, H.: Concurrency for mobile object net systems. Fundamenta Informaticae 54(2-3), 221–235 (2003)
Llorens, M., Oliver, J.: Structural and Dynamic Changes in Concurrent Systems: Reconfigurable Petri Nets. IEEE Transactions on Computers 53(9), 1147–1158 (2004)
Meseguer, J., Montanari, U.: Petri Nets Are Monoids. Information and Computation 88(2), 105–155 (1990)
Murata, T.: Petri nets: Properties, analysis and applications. In: Proc. IEEE, vol. 77, pp. 541–580. IEEE Computer Society Press, Los Alamitos (1989)
Padberg, J., Gajewsky, M., Ermel, C.: Rule-based refinement of high-level nets preserving safety properties. Science of Computer Programming 40(1), 97–118 (2001)
Padberg, J., Hoffmann, K., Ehrig, H., Modica, T., Biermann, E., Ermel, C.: Maintaining Consistency in Layered Architectures of Mobile Ad-hoc Networks. In: FASE 2007, LNCS, vol. 4422, pp. 383–397, Springer, Heidleberg (2007)
Padberg, J., Urbášek, M.: Rule-Based Refinement of Petri Nets: A Survey. In: Ehrig, H., Reisig, W., Rozenberg, G., Weber, H. (eds.) Petri Net Technology for Communication-Based Systems. LNCS, vol. 2472, pp. 161–196. Springer, Heidelberg (2003)
Parisi-Presicce, F.: A Formal Framework for Petri Net Class Transformations. In: Ehrig, H., Reisig, W., Rozenberg, G., Weber, H. (eds.) Petri Net Technology for Communication-Based Systems. LNCS, vol. 2472, pp. 409–430. Springer, Heidelberg (2003)
Rozenberg, G.: Handbook of Graph Grammars and Computing by Graph Transformations, Volume 1: Foundations. World Scientific, Singapore (1997)
Urbášek, M.: Categorical Net Transformations for Petri Net Technology. PhD thesis, Technische Universität Berlin (2003)
Valk, R.: Petri Nets as Token Objects: An Introduction to Elementary Object Nets. In: Desel, J., Silva, M. (eds.) ICATPN 1998. LNCS, vol. 1420, pp. 1–25. Springer, Heidelberg (1998)
van der Aalst, W.M.P.: The Application of Petri Nets to Workflow Management. Journal of Circuits, Systems and Computers 8(1), 21–66 (1998)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Ehrig, H., Hoffmann, K., Padberg, J., Prange, U., Ermel, C. (2007). Independence of Net Transformations and Token Firing in Reconfigurable Place/Transition Systems. In: Kleijn, J., Yakovlev, A. (eds) Petri Nets and Other Models of Concurrency – ICATPN 2007. ICATPN 2007. Lecture Notes in Computer Science, vol 4546. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73094-1_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-73094-1_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73093-4
Online ISBN: 978-3-540-73094-1
eBook Packages: Computer ScienceComputer Science (R0)