Abstract
In this paper, we reconsider an old and simple notion of parallel graph transformation and point out various perspectives concerning the parallel generation of graph languages, the parallelization of graph algorithms, the parallel transformation of infinite graphs, and parallel models of computation.
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Ehrig, H., Kreowski, H.-J.: Parallelism of manipulations in multidimensional information structures. In: Mazurkiewicz, A. (ed.) MFCS 1976. LNCS, vol. 45, pp. 284–293. Springer, Heidelberg (1976). https://doi.org/10.1007/3-540-07854-1_188
Corradini, A., Ehrig, H., Heckel, R., Löwe, M., Montanari, U., Rossi, F.: Algebraic approaches to graph transformation part I: basic concepts and double pushout approach. In: Rozenberg [34], pp. 163–245
Baldan, P., Corradini, A., Ehrig, H., Löwe, M., Montanari, U., Rossi, F.: Concurrent semantics of algebraic graph transformations. In: Ehrig et al. [5], pp. 107–185
Kreowski, H.-J.: Manipulationen von Graphmanipulationen. Ph.D. thesis, Technische Universität Berlin (1978). Fachbereich Informatik
Ehrig, H., Kreowski, H.-J., Montanari, U., Rozenberg, G. (eds.): Handbook of graph grammars and computing by graph transformation, concurrency, parallelism, and distribution, vol. 3. World Scientific, Singapore (1999)
Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of algebraic graph transformation. monographs in theoretical computer science. An EATCS Series. Springer, Heidelberg (2006). https://doi.org/10.1007/3-540-31188-2
Ehrig, H., Ermel, C., Golas, U., Hermann, F.: Graph and model transformation: general framework and applications. monographs in theoretical computer science. An EATCS Series. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47980-3
Löwe, M.: Algebraic approach to single-pushout graph transformation. Theor. Comput. Sci. 109, 181–224 (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). https://doi.org/10.1007/11841883_4
Habel, A., Kreowski, H.-J.: Some structural aspects of hypergraph languages generated by hyperedge replacement. In: Brandenburg, F.J., Vidal-Naquet, G., Wirsing, M. (eds.) STACS 1987. LNCS, vol. 247, pp. 207–219. Springer, Heidelberg (1987). https://doi.org/10.1007/BFb0039608
Habel, A.: Hyperedge Replacement: Grammars and Languages. LNCS, vol. 643. Springer, Berlin (1992)
Drewes, F., Habel, A., Kreowski, H.-J.: Hyperedge replacement graph grammars. In: Rozenberg [34], pp. 95–162
Engelfriet, J.: Context-free graph grammars. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, pp. 125–213. Springer, Heidelberg (1997). https://doi.org/10.1007/978-3-642-59126-6_3
Kreowski, H.-J., Klempien-Hinrichs, R., Kuske, S.: Some essentials of graph transformation. In: Esik, Z., Martin-Vide, C., Mitrana, V. (eds.) Recent Advances in Formal Languages and Applications. Studies in Computational Intelligence, vol. 25, pp. 229–254. Springer, Heidelberg (2006). https://doi.org/10.1007/978-3-540-33461-3_9
Rozenberg, G., Salomaa, A.: The Mathematical Theory of \(L\) Systems. Pure and Applied Mathematics: A Series of Monographs and Textbooks, vol. 90. Academic Press, Orlando (1980)
Kreowski, H.-J., Kuske, S., Lye, A.: Fusion grammars: a novel approach to the generation of graph languages. In: de Lara, J., Plump, D. (eds.) ICGT 2017. LNCS, vol. 10373, pp. 90–105. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-61470-0_6
Floyd, R.W.: Algorithm 97 (shortest path). Commun. ACM 5(6), 345 (1962)
Warshall, S.: A theorem on Boolean matrices. J. ACM 9(1), 11–12 (1962)
Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1(1), 269–271 (1959)
Mahr, B.: Algebraic complexity of path problems. RAIRO Theor. Inf. Appl. 16(3), 263–292 (1982)
Litovski, I., Métivier, Y., Sopena, É.: Graph relabelling systems and distributed algorithms. In: Ehrig et al. [5], pp. 1–56
Kreowski, H.-J., Kuske, S.: Graph multiset transformation - a new framework for massively parallel computation inspired by DNA computing. Nat. Comput. 10(2), 961–986 (2011). https://doi.org/10.1007/s11047-010-9245-6
Diestel, R. (ed.): Directions in Infinite Graph Theory and Combinatorics. Topics in Discrete Mathematics, vol. 3. Elsevier, North Holland (1992)
Codd, E.F.: Cellular Automata. Academic Press, New York (1968)
Kari, J.: Theory of cellular automata: a survey. Theoret. Comput. Sci. 334, 3–33 (2005)
von Neumann, J.: The General and Logical Theory of Automata, pp. 1–41. Wiley, Pasadena (1951)
Wolfram, S.: A New Kind of Science. Wolfram Media Inc., Champaign (2002)
Peitgen, H.-O., Jürgens, H., Saupe, D.: Chaos and Fractals: New Frontiers of Science. Springer, New York (1992). https://doi.org/10.1007/978-1-4757-4740-9
Kreowski, H.-J.: A comparison between Petri nets and graph grammars. In: Noltemeier, H. (ed.) WG 1980. LNCS, vol. 100, pp. 306–317. Springer, Heidelberg (1981). https://doi.org/10.1007/3-540-10291-4_22
Corradini, A., Montanari, U., Rossi, F.: Graph processes. Fundam. Inform. 26(3/4), 241–265 (1996)
Dashkovskiy, S., Kreowski, H.-J., Kuske, S., Mironchenko, A., Naujuk, L., von Totth, C.: Production networks as communities of autonomous units and their stability. Int. Electron. J. Pure Appl. Math. 2, 17–42 (2010)
Abdenebaoui, L., Kreowski, H.-J., Kuske, S.: Graph-transformational swarms. In: Bensch, S., Drewes, F., Freund, R., Otto, F., (eds.) Proceedings of the Fifth Workshop on Non-Classical Models for Automata and Applications (NCMA 2013), pp. 35–50. Österreichische Computer Gesellschaft (2013)
Hölscher, K., Kreowski, H.-J., Kuske, S.: Autonomous units to model interacting sequential and parallel processes. Fundam. Inform. 92, 233–257 (2009)
Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformation. Foundations, vol. 1. World Scientific, Singapore (1997)
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We are grateful to the four reviewers for their helpful comments that lead to various improvements.
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Kreowski, HJ., Kuske, S., Lye, A. (2018). A Simple Notion of Parallel Graph Transformation and Its Perspectives. In: Heckel, R., Taentzer, G. (eds) Graph Transformation, Specifications, and Nets. Lecture Notes in Computer Science(), vol 10800. Springer, Cham. https://doi.org/10.1007/978-3-319-75396-6_4
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DOI: https://doi.org/10.1007/978-3-319-75396-6_4
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