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. For the transformation of Petri nets in the double pushout approach, the categorical framework of adhesive high-level replacement systems has been instantiated to Petri nets. In this paper, we show that also place/transition systems form a weak adhesive high-level replacement category. This allows us to apply the developed theory also to tranformations within reconfigurable place/transition systems.
This work has been partly funded by the research project for MAℓNET of the German Research Council (see http://tfs.cs.tu-berlin.de/formalnet/).
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References
Meseguer, J., Montanari, U.: Petri Nets are Monoids. Information and Computation 88(2), 105–155 (1990)
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)
Ehrig, H., Hoffmann, K., Padberg, J., Prange, U., Ermel, C.: Independence of Net Transformations and Token Firing in Reconfigurable Place/Transition Systems. In: Kleijn, J., Yakovlev, A. (eds.) ICATPN 2007. LNCS, vol. 4546, pp. 104–123. Springer, Heidelberg (2007)
Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. EATCS Monographs. Springer, Heidelberg (2006)
Ehrig, H., Habel, A., Padberg, J., Prange, U.: Adhesive High-Level Replacement Systems: A New Categorical Framework for Graph Transformation. Fundamenta Informaticae 74(1), 1–29 (2006)
Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformation: Foundations, vol. 1. World Scientific, Singapore (1997)
Lack, S., Sobociński, P.: Adhesive and Quasiadhesive Categories. Theoretical Informatics and Applications 39(3), 511–546 (2005)
Prange, U.: Algebraic High-Level Nets as Weak Adhesive HLR Categories. Electronic Communications of the EASST 2, 1–13 (2007)
Reisig, W.: Petri Nets. EATCS Monographs on Theoretical Computer Science, vol. 4. Springer, Berlin (1985)
Nielsen, M., Rozenberg, G., Thiagarajan, P.S.: Elementary Transition Systems. Theoretical Computer Science 96(1), 3–33 (1992)
Ehrig, H.: Introduction to the Algebraic Theory of Graph Grammars (A Survey). In: Ng, E.W., Ehrig, H., Rozenberg, G. (eds.) Graph Grammars 1978. LNCS, vol. 73, pp. 1–69. Springer, Heidelberg (1979)
Billington, J.: Extensions to Coloured Petri Nets. In: Proceedings of PNPM 1989, pp. 61–70. IEEE, Los Alamitos (1989)
Campos, J., Sánchez, B., Silva, M.: Throughput Lower Bounds for Markovian Petri Nets: Transformation Techniques. In: Proceedings of PNPM 1991, pp. 322–331. IEEE, Los Alamitos (1991)
Urbášek, M.: Categorical Net Transformations for Petri Net Technology. PhD thesis, TU Berlin (2003)
Belli, F., Dreyer, J.: Systems Modelling and Simulation by Means of Predicate/Transition Nets and Logic Programming. In: Proceedings of IEA/AIE 1994, pp. 465–474 (1994)
Bessey, T., Becker, M.: Comparison of the Modeling Power of Fluid Stochastic Petri Nets (FSPN) and Hybrid Petri Nets (HPN). In: Proceedings of SMC 2002, vol. 2, pp. 354–358. IEEE, Los Alamitos (2002)
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)
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)
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)
Corts, 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)
Haddad, S.: A Reduction Theory for Coloured Nets. In: Rozenberg, G. (ed.) APN 1989. LNCS, vol. 424, pp. 209–235. Springer, Heidelberg (1990)
Desel, J.: On Abstraction of Nets. In: Rozenberg, G. (ed.) APN 1991. LNCS, vol. 524, pp. 78–92. Springer, Heidelberg (1991)
Esparza, J., Silva, M.: On the Analysis and Synthesis of Free Choice Systems. In: Rozenberg, G. (ed.) APN 1990. LNCS, vol. 483, pp. 243–286. Springer, Heidelberg (1991)
Chehaibar, G.: Replacement of Open Interface Subnets and Stable State Transformation Equivalence. In: Rozenberg, G. (ed.) APN 1993. LNCS, vol. 674, pp. 1–25. Springer, Heidelberg (1993)
Bonhomme, P., Aygalinc, P., Berthelot, G., Calvez, S.: Hierarchical Control of Time Petri Nets by Means of Transformations. In: Proceedings of SMC 2002, vol. 4, pp. 6–11. IEEE Computer Society Press, Los Alamitos (2002)
Berthelot, G.: Checking Properties of Nets Using Transformation. In: Rozenberg, G. (ed.) APN 1985. LNCS, vol. 222, pp. 19–40. Springer, Heidelberg (1986)
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)
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)
Murata, T.: Petri Nets: Properties, Analysis and Applications. In: Proceedings of the IEEE, vol. 77, pp. 541–580. IEEE Computer Society Press, Los Alamitos (1989)
Best, E., Devillers, R., Koutny, M.: The Box Algebra = Petri Nets + Process Expressions. Information and Computation 178(1), 44–100 (2002)
van der Aalst, W.: The Application of Petri Nets to Workflow Management. Journal of Circuits, Systems and Computers 8(1), 21–66 (1998)
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., 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)
Baldan, P., Corradini, A., Ehrig, H., Heckel, R., König, B.: Bisimilarity and Behaviour-Preserving Reconfigurations of Open Petri Nets. In: Mossakowski, T., Montanari, U., Haveraaen, M. (eds.) CALCO 2007. LNCS, vol. 4624, pp. 126–142. Springer, Heidelberg (2007)
Balbo, G., Bruell, S., Sereno, M.: Product Form Solution for Generalized Stochastic Petri Nets. IEEE Transactions on Software Engineering 28(10), 915–932 (2002)
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)
Cheung, T., Lu, Y.: Five Classes of Invariant-Preserving Transformations on Colored Petri Nets. In: Donatelli, S., Kleijn, J. (eds.) ICATPN 1999. LNCS, vol. 1639, pp. 384–403. Springer, Heidelberg (1999)
Esparza, J.: Model Checking Using Net Unfoldings. Science of Computer Programming 23(2-3), 151–195 (1994)
Padberg, J., Hoffmann, K., Ehrig, H., Modica, T., Biermann, E., Ermel, C.: Maintaining Consistency in Layered Architectures of Mobile Ad-hoc Networks. In: Dwyer, M.B., Lopes, A. (eds.) FASE 2007. LNCS, vol. 4422, pp. 383–397. Springer, Heidelberg (2007)
Llorens, M., Oliver, J.: Structural and Dynamic Changes in Concurrent Systems: Reconfigurable Petri Nets. IEEE Transactions on Computers 53(9), 1147–1158 (2004)
AGG Homepage (2007), http://tfs.cs.tu-berlin.de/agg
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)
Lambers, L., Ehrig, H., Prange, U., Orejas, F.: Parallelism and Concurrency in Adhesive High-Level Replacement Systems with Negative Application Conditions. Electronic Notes in Theoretical Computer Science (to appear 2008)
Padberg, J., Ehrig, H., Ribeiro, L.: Algebraic High-Level Net Transformation Systems. Mathematical Structures in Computer Science 5(2), 217–256 (1995)
Prange, U.: Algebraic High-Level Systems as Weak Adhesive HLR Categories. Electronic Notes in Theoretical Computer Science (to appear, 2008)
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Prange, U., Ehrig, H., Hoffmann, K., Padberg, J. (2008). Transformations in Reconfigurable Place/Transition Systems. In: Degano, P., De Nicola, R., Meseguer, J. (eds) Concurrency, Graphs and Models. Lecture Notes in Computer Science, vol 5065. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68679-8_7
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DOI: https://doi.org/10.1007/978-3-540-68679-8_7
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