Abstract
We tackle the problem of graph transformation with particular focus on node cloning. We propose a new approach to graph rewriting, called polarized node cloning, where a node may be cloned together with either all its incident edges or with only its outgoing edges or with only its incoming edges or with none of its incident edges. We thus subsume previous works such as the sesqui-pushout, the heterogeneous pushout and the adaptive star grammars approaches. We first define polarized node cloning algorithmically, then we propose an algebraic definition. We use polarization annotations to declare how a node must be cloned. For this purpose, we introduce the notion of polarized graphs as graphs endowed with some annotations on nodes and we define graph transformations with polarized node cloning by means of sesqui-pushouts in the category of polarized graphs.
This work has been funded by the project CLIMT of the French Agence Nationale de la Recherche (ANR-11-BS02-016).
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References
Baader, F., Nipkow, T.: Term rewriting and all that. Cambridge University Press (1998)
Barendregt, H.P., van Eekelen, M.C.J.D., Glauert, J.R.W., Kenneway, J.R., Plasmeijer, M.J., Sleep, M.R.: Term Graph Rewriting. In: de Bakker, J.W., Nijman, A.J., Treleaven, P.C. (eds.) PARLE 1987. LNCS, vol. 259, pp. 141–158. Springer, Heidelberg (1987)
Book, R.V., Otto, F.: String-rewriting systems. Springer (1993)
Corradini, A., Heindel, T., Hermann, F., König, B.: Sesqui-Pushout Rewriting. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 30–45. Springer, Heidelberg (2006)
Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Algebraic approaches to graph transformation - part I: Basic concepts and double pushout approach. In: Handbook of Graph Grammars, pp. 163–246 (1997)
Drewes, F., Hoffmann, B., Janssens, D., Minas, M., Van Eetvelde, N.: Adaptive Star Grammars. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 77–91. Springer, Heidelberg (2006)
Duval, D., Echahed, R., Prost, F.: A Heterogeneous Pushout Approach to Term-Graph Transformation. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 194–208. Springer, Heidelberg (2009)
Duval, D., Echahed, R., Prost, F.: Graph rewriting with polarized cloning. arXiv:0911.3786,V3 (2012)
Dyckhoff, R., Tholen, W.: Exponentiable morphisms, partial products and pullback complements. Journal of Pure and Applied Algebra (1987)
Echahed, R.: Inductively Sequential Term-Graph Rewrite Systems. In: Ehrig, H., Heckel, R., Rozenberg, G., Taentzer, G. (eds.) ICGT 2008. LNCS, vol. 5214, pp. 84–98. Springer, Heidelberg (2008)
Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.): Handbook of Graph Grammars and Computing by Graph Transformations. Applications, Languages and Tools, vol. 2. World Scientific (1999)
Ehrig, H., Heckel, R., Korff, M., Löwe, M., Ribeiro, L., Wagner, A., Corradini, A.: Algebraic approaches to graph transformation - part II: Single pushout approach and comparison with double pushout approach. In: Handbook of Graph Grammars, pp. 247–312 (1997)
Ehrig, H., Kreowski, H.-J., Montanari, U., Rozenberg, G. (eds.): Handbook of Graph Grammars and Computing by Graph Transformations. Concurrency, Parallelism and Distribution, vol. 3. World Scientific (1999)
Ehrig, H., Pfender, M., Schneider, H.J.: Graph-grammars: An algebraic approach. In: 14th Annual Symposium on Foundations of Computer Science (FOCS), The University of Iowa, USA, October 15-17, pp. 167–180. IEEE (1973)
Gosling, J., Joy, B., Steele, G., Bracha, G., Buckley, A.: The Java(TM) Language Specification, Java SE 7 edn. Oracle documentation (2005)
Kennaway, R.: On “on graph rewritings”. Theoretical Computer Science 52, 37–58 (1987)
Löwe, M.: Algebraic approach to single-pushout graph transformation. Theoretical Computer Science 109(1&2), 181–224 (1993)
Löwe, M.: Graph Rewriting in Span-Categories. In: Ehrig, H., Rensink, A., Rozenberg, G., Schürr, A. (eds.) ICGT 2010. LNCS, vol. 6372, pp. 218–233. Springer, Heidelberg (2010)
Mac Lane, S.: Categories for the Working Mathematician, 2nd edn., vol. 5. Springer (1998)
Miller, F., Vandome, A., McBrewster, J.: Eiffel (programming language). Alphascript Publishing (2010)
Raoult, J.C.: On graph rewriting. Theoretical Computer Science 32, 1–24 (1984)
Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformations. Foundations, vol. 1. World Scientific (1997)
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Duval, D., Echahed, R., Prost, F. (2012). Graph Transformation with Focus on Incident Edges. In: Ehrig, H., Engels, G., Kreowski, HJ., Rozenberg, G. (eds) Graph Transformations. ICGT 2012. Lecture Notes in Computer Science, vol 7562. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33654-6_11
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