Abstract
Controlled graph rewriting enhances expressiveness of plain graph-rewriting systems (i.e., sets of graph-rewriting rules) by introducing additional constructs for explicitly controlling graph-rewriting rule applications. In this regard, a formal semantic foundation for controlled graph rewriting is inevitable as a reliable basis for tool-based specification and automated analysis of graph-based algorithms. Although several promising attempts have been proposed in the literature, a comprehensive theory of controlled graph rewriting capturing semantic subtleties of advanced control constructs provided by practical tools is still an open challenge. In this paper, we propose graph-rewriting Petri nets (GPN) as a novel foundation for unifying control-flow and rule-application semantics of controlled graph rewriting. GPN instantiate coloured Petri nets with categorical DPO-based graph-rewriting theory where token colours denote typed graphs and graph morphisms and transitions define templates for guarded graph-rewriting rule applications. Hence, GPN enjoy the rich body of specification and analysis techniques of Petri nets including inherent notions of concurrency. To demonstrate expressiveness of GPN, we present a case study by means of a topology-control algorithm for wireless sensor networks.
This work has been partially funded by the German Research Foundation (DFG) as part of project A1 within CRC1053–MAKI.
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References
Baldan, P., Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Löwe, M.: Concurrent semantics of algebraic graph transformation. In: Handbook of Graph Grammars and Computing by Graph Transformation, vol. 3, pp. 107–187. World Scientific (1999). https://doi.org/10.1142/9789812814951_0003
Bunke, H.: Programmed graph grammars. In: Claus, V., Ehrig, H., Rozenberg, G. (eds.) Graph Grammars 1978. LNCS, vol. 73, pp. 155–166. Springer, Heidelberg (1979). https://doi.org/10.1007/BFb0025718
Corradini, A., Ehrig, H., Löwe, M., Montanari, U., Rossi, F.: Abstract graph derivations in the double pushout approach. In: Schneider, H.J., Ehrig, H. (eds.) Graph Transformations in Computer Science. LNCS, vol. 776, pp. 86–103. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-57787-4_6
Corradini, A., Montanari, U., Rossi, F.: Graph processes. Fundamenta Informaticae 26(3–4), 241–265 (1996). https://doi.org/10.3233/FI-1996-263402
Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Springer, Heidelberg (2006). https://doi.org/10.1007/3-540-31188-2
Esparza, J.: Decidability and complexity of Petri net problems — an introduction. In: Reisig, W., Rozenberg, G. (eds.) ACPN 1996. LNCS, vol. 1491, pp. 374–428. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-65306-6_20
Fischer, T., Niere, J., Torunski, L., Zündorf, A.: Story diagrams: a new graph rewrite language based on the unified modeling language and Java. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) TAGT 1998. LNCS, vol. 1764, pp. 296–309. Springer, Heidelberg (2000). https://doi.org/10.1007/978-3-540-46464-8_21
Ghamarian, A.H., de Mol, M.J., Rensink, A., Zambon, E., Zimakova, M.V.: Modelling and analysis using GROOVE. Int. J. Softw. Tools Technol. Transf. 14, 15–40 (2012). https://doi.org/10.1007/s10009-011-0186-x
Guerra, E., de Lara, J.: Colouring: execution, debug and analysis of QVT-relations transformations through coloured petri nets. Softw. Syst. Model. 13(4), 1447–1472 (2014). https://doi.org/10.1007/s10270-012-0292-6
Hoffmann, K., Mossakowski, T.: Algebraic higher-order nets: graphs and petri nets as tokens. In: Wirsing, M., Pattinson, D., Hennicker, R. (eds.) WADT 2002. LNCS, vol. 2755, pp. 253–267. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-40020-2_14
Jensen, K., Kristensen, L.M.: Coloured Petri Nets: Modelling and Validation of Concurrent Systems. Springer Science & Business Media, Heidelberg (2009). https://doi.org/10.1007/b95112
Kluge, R., Stein, M., Varró, G., Schürr, A., Hollick, M., Mühlhäuser, M.: A systematic approach to constructing families of incremental topology control algorithms using graph transformation. Softw. Syst. Model. 1–41 (2017). https://doi.org/10.1007/s10270-017-0587-8
Kreowski, H.-J., Kuske, S., Rozenberg, G.: Graph transformation units – an overview. In: Degano, P., De Nicola, R., Meseguer, J. (eds.) Concurrency, Graphs and Models. LNCS, vol. 5065, pp. 57–75. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-68679-8_5
Leblebici, E., Anjorin, A., Schürr, A.: Developing eMoflon with eMoflon. In: Di Ruscio, D., Varró, D. (eds.) ICMT 2014. LNCS, vol. 8568, pp. 138–145. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08789-4_10
Li, M., Li, Z., Vasilakos, A.V.: A survey on topology control in wireless sensor networks: taxonomy, comparative study, and open issues. Proc. IEEE 101(12), 2538–2557 (2013). https://doi.org/10.1109/JPROC.2013.2257631
Plump, D., Steinert, S.: The semantics of graph programs. In: RULE 2009 (2009). https://doi.org/10.4204/EPTCS.21.3
Schürr, A.: Logic-based programmed structure rewriting systems. Fundam. Inf. 26(3,4), 363–385 (1996). https://doi.org/10.3233/FI-1996-263407
Schürr, A., Winter, A.J., Zündorf, A.: The PROGRES-approach: language and environment. In: Handbook of Graph Grammars and Computing by Graph Transformation, vol. 2, pp. 487–550. World Scientific (1999). https://doi.org/10.1142/9789812815149_0013
Strüber, D., Born, K., Gill, K.D., Groner, R., Kehrer, T., Ohrndorf, M., Tichy, M.: Henshin: a usability-focused framework for EMF model transformation development. In: de Lara, J., Plump, D. (eds.) ICGT 2017. LNCS, vol. 10373, pp. 196–208. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-61470-0_12
Wimmer, M., Kappel, G., Kusel, A., Retschitzegger, W., Schönböck, J., Schwinger, W.: Right or wrong?–verification of model transformations using colored petri nets. In: DSM 2009 (2009)
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Kulcsár, G., Lochau, M., Schürr, A. (2018). Graph-Rewriting Petri Nets. In: Lambers, L., Weber, J. (eds) Graph Transformation. ICGT 2018. Lecture Notes in Computer Science(), vol 10887. Springer, Cham. https://doi.org/10.1007/978-3-319-92991-0_6
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