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Modular Termination of Graph Transformation

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Graph Transformation, Specifications, and Nets

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10800))

Abstract

We establish a machine-checkable condition which ensures that the union of two terminating hypergraph transformation systems is terminating. The condition is based on so-called sequential critical pairs which represent consecutive rule applications that are not independent. In contrast to a corresponding modularity result for term rewriting, no restrictions on the form of rules are required. Our result applies to both systems with injective rules and systems with rules that merge nodes or edges.

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References

  1. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)

    Book  MATH  Google Scholar 

  2. Bezem, M., Klop, J.W., de Vrijer, R. (eds.): Term Rewriting Systems. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  3. Bruggink, H.J.S.: Towards a systematic method for proving termination of graph transformation systems. Electron. Notes Theor. Comput. Sci. 213(1), 23–38 (2008). https://doi.org/10.1016/j.entcs.2008.04.072

    Article  MATH  Google Scholar 

  4. Bruggink, H.J.S., König, B., Nolte, D., Zantema, H.: Proving termination of graph transformation systems using weighted type graphs over semirings. In: Parisi-Presicce, F., Westfechtel, B. (eds.) ICGT 2015. LNCS, vol. 9151, pp. 52–68. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21145-9_4

    Chapter  Google Scholar 

  5. Bruggink, H.J.S., König, B., Zantema, H.: Termination analysis for graph transformation systems. In: Diaz, J., Lanese, I., Sangiorgi, D. (eds.) TCS 2014. LNCS, vol. 8705, pp. 179–194. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44602-7_15

    Google Scholar 

  6. Courcelle, B.: Graph rewriting: an algebraic and logic approach. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. B, Chap. 5. Elsevier (1990)

    Google Scholar 

  7. Dershowitz, N.: Termination of linear rewriting systems (preliminary version). In: Even, S., Kariv, O. (eds.) ICALP 1981. LNCS, vol. 115, pp. 448–458. Springer, Heidelberg (1981). https://doi.org/10.1007/3-540-10843-2_36

    Chapter  Google Scholar 

  8. 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

    Chapter  Google Scholar 

  9. Ehrig, H., Rosen, B.K.: Commutativity of independent transformations on complex objects. Research Report RC 6251. IBM Thomas J. Watson Research Center, Yorktown Heights (1976)

    Google Scholar 

  10. Habel, A.: Hyperedge Replacement: Grammars and Languages. LNCS, vol. 643. Springer, Heidelberg (1992). https://doi.org/10.1007/BFb0013875

    MATH  Google Scholar 

  11. Habel, A., Müller, J., Plump, D.: Double-pushout graph transformation revisited. Math. Struct. Comput. Sci. 11(5), 637–688 (2001). https://doi.org/10.1017/S0960129501003425

    Article  MathSciNet  MATH  Google Scholar 

  12. Hoffmann, B., Plump, D.: Implementing term rewriting by jungle evaluation. RAIRO Theor. Inform. Appl. 25(5), 445–472 (1991). https://doi.org/10.1051/ita/1991250504451

    Article  MathSciNet  MATH  Google Scholar 

  13. Hristakiev, I., Plump, D.: Towards critical pair analysis for the graph programming language GP 2. In: James, P., Roggenbach, M. (eds.) WADT 2016. LNCS, vol. 10644, pp. 153–169. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-72044-9_11

    Chapter  Google Scholar 

  14. Krishna Rao, M.R.K.: Modular aspects of term graph rewriting. Theor. Comput. Sci. 208(1–2), 59–86 (1998). https://doi.org/10.1016/S0304-3975(98)00079-6

    MathSciNet  MATH  Google Scholar 

  15. Plump, D.: Implementing term rewriting by graph reduction: termination of combined systems. In: Kaplan, S., Okada, M. (eds.) CTRS 1990. LNCS, vol. 516, pp. 307–317. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-54317-1_100

    Chapter  Google Scholar 

  16. Plump, D.: On termination of graph rewriting. In: Nagl, M. (ed.) WG 1995. LNCS, vol. 1017, pp. 88–100. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-60618-1_68

    Chapter  Google Scholar 

  17. Plump, D.: Simplification orders for term graph rewriting. In: Prívara, I., Ružička, P. (eds.) MFCS 1997. LNCS, vol. 1295, pp. 458–467. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0029989

    Chapter  Google Scholar 

  18. Plump, D.: Termination of graph rewriting is undecidable. Fundam. Inform. 33(2), 201–209 (1998). https://doi.org/10.3233/FI-1998-33204

    MathSciNet  MATH  Google Scholar 

  19. Plump, D.: Computing by Graph Rewriting. Habilitation thesis, Universität Bremen, Fachbereich Mathematik und Informatik (1999)

    Google Scholar 

  20. Plump, D.: Confluence of graph transformation revisited. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds.) Processes, Terms and Cycles: Steps on the Road to Infinity. LNCS, vol. 3838, pp. 280–308. Springer, Heidelberg (2005). https://doi.org/10.1007/11601548_16

    Chapter  Google Scholar 

  21. Sabel, D., Zantema, H.: Termination of cycle rewriting by transformation and matrix interpretation. Log. Methods Comput. Sci. 13(1), 38 (2017). https://doi.org/10.23638/LMCS-13(1:11)2017

    MathSciNet  MATH  Google Scholar 

  22. Toyama, Y.: Counterexamples to termination for the direct sum of term rewriting systems. Inf. Process. Lett. 25, 141–143 (1987). https://doi.org/10.1016/0020-0190(87)90122-0

    Article  MathSciNet  MATH  Google Scholar 

  23. Zantema, H., König, B., Bruggink, H.J.S.: Termination of cycle rewriting. In: Dowek, G. (ed.) RTA-TLCA 2014. LNCS, vol. 8560, pp. 476–490. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08918-8_33

    Google Scholar 

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Plump, D. (2018). Modular Termination of Graph Transformation. 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_13

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  • DOI: https://doi.org/10.1007/978-3-319-75396-6_13

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  • Online ISBN: 978-3-319-75396-6

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