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A Simple Notion of Parallel Graph Transformation and Its Perspectives

  • Hans-Jörg Kreowski
  • Sabine Kuske
  • Aaron LyeEmail author
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10800)

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.

Notes

Acknowledgment

We are grateful to the four reviewers for their helpful comments that lead to various improvements.

References

  1. 1.
    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 CrossRefGoogle Scholar
  2. 2.
    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. 163–245Google Scholar
  3. 3.
    Baldan, P., Corradini, A., Ehrig, H., Löwe, M., Montanari, U., Rossi, F.: Concurrent semantics of algebraic graph transformations. In: Ehrig et al. [5], pp. 107–185Google Scholar
  4. 4.
    Kreowski, H.-J.: Manipulationen von Graphmanipulationen. Ph.D. thesis, Technische Universität Berlin (1978). Fachbereich InformatikGoogle Scholar
  5. 5.
    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)zbMATHGoogle Scholar
  6. 6.
    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 zbMATHGoogle Scholar
  7. 7.
    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 CrossRefzbMATHGoogle Scholar
  8. 8.
    Löwe, M.: Algebraic approach to single-pushout graph transformation. Theor. Comput. Sci. 109, 181–224 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    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 CrossRefGoogle Scholar
  10. 10.
    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 CrossRefGoogle Scholar
  11. 11.
    Habel, A.: Hyperedge Replacement: Grammars and Languages. LNCS, vol. 643. Springer, Berlin (1992)zbMATHGoogle Scholar
  12. 12.
    Drewes, F., Habel, A., Kreowski, H.-J.: Hyperedge replacement graph grammars. In: Rozenberg [34], pp. 95–162Google Scholar
  13. 13.
    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 CrossRefGoogle Scholar
  14. 14.
    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 CrossRefGoogle Scholar
  15. 15.
    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)zbMATHGoogle Scholar
  16. 16.
    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 CrossRefGoogle Scholar
  17. 17.
    Floyd, R.W.: Algorithm 97 (shortest path). Commun. ACM 5(6), 345 (1962)CrossRefGoogle Scholar
  18. 18.
    Warshall, S.: A theorem on Boolean matrices. J. ACM 9(1), 11–12 (1962)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1(1), 269–271 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Mahr, B.: Algebraic complexity of path problems. RAIRO Theor. Inf. Appl. 16(3), 263–292 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Litovski, I., Métivier, Y., Sopena, É.: Graph relabelling systems and distributed algorithms. In: Ehrig et al. [5], pp. 1–56Google Scholar
  22. 22.
    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 MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Diestel, R. (ed.): Directions in Infinite Graph Theory and Combinatorics. Topics in Discrete Mathematics, vol. 3. Elsevier, North Holland (1992)zbMATHGoogle Scholar
  24. 24.
    Codd, E.F.: Cellular Automata. Academic Press, New York (1968)zbMATHGoogle Scholar
  25. 25.
    Kari, J.: Theory of cellular automata: a survey. Theoret. Comput. Sci. 334, 3–33 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    von Neumann, J.: The General and Logical Theory of Automata, pp. 1–41. Wiley, Pasadena (1951)Google Scholar
  27. 27.
    Wolfram, S.: A New Kind of Science. Wolfram Media Inc., Champaign (2002)zbMATHGoogle Scholar
  28. 28.
    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 CrossRefzbMATHGoogle Scholar
  29. 29.
    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 CrossRefGoogle Scholar
  30. 30.
    Corradini, A., Montanari, U., Rossi, F.: Graph processes. Fundam. Inform. 26(3/4), 241–265 (1996)MathSciNetzbMATHGoogle Scholar
  31. 31.
    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)zbMATHGoogle Scholar
  32. 32.
    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)Google Scholar
  33. 33.
    Hölscher, K., Kreowski, H.-J., Kuske, S.: Autonomous units to model interacting sequential and parallel processes. Fundam. Inform. 92, 233–257 (2009)MathSciNetzbMATHGoogle Scholar
  34. 34.
    Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformation. Foundations, vol. 1. World Scientific, Singapore (1997)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of BremenBremenGermany

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