Advertisement

Towards Critical Pair Analysis for the Graph Programming Language GP 2

  • Ivaylo Hristakiev
  • Detlef Plump
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10644)

Abstract

We present the foundations of critical pair analysis for the graph programming language GP 2. Our goal is to develop a static checker that can prove or refute confluence (functional behaviour) for a large class of graph programs. In this paper, we introduce symbolic critical pairs of GP 2 rule schemata, which are labelled with expressions, and establish the completeness and finiteness of the set of symbolic critical pairs over a finite set of rule schemata. We give a procedure for their construction.

References

  1. 1.
    Baader, F., Snyder, W.: Unification theory. In: Robinson, J.A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. 2, pp. 445–532. Elsevier and MIT Press, Amsterdam and Cambridge (2001)CrossRefGoogle Scholar
  2. 2.
    Bak, C.: GP 2: efficient implementation of a graph programming language. Ph.D. thesis, University of York (2015). http://etheses.whiterose.ac.uk/id/eprint/12586
  3. 3.
    Duffin, R.J.: Topology of series-parallel networks. J. Math. Anal. Appl. 10(2), 303–318 (1965).  https://doi.org/10.1016/0022-247X(65)90125-3 MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Monographs in Theoretical Computer Science. Springer, Heidelberg (2006).  https://doi.org/10.1007/3-540-31188-2 zbMATHGoogle Scholar
  5. 5.
    Ehrig, H., Golas, U., Habel, A., Lambers, L., Orejas, F.: \(\cal{M}\)-adhesive transformation systems with nested application conditions: part 2: embedding, critical pairs and local confluence. Fundamenta Informaticae 118(1–2), 35–63 (2012).  https://doi.org/10.3233/FI-2012-705 MathSciNetzbMATHGoogle Scholar
  6. 6.
    Ehrig, H., Prange, U., Taentzer, G.: Fundamental theory for typed attributed graph transformation. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds.) ICGT 2004. LNCS, vol. 3256, pp. 161–177. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-30203-2_13 CrossRefGoogle Scholar
  7. 7.
    Golas, U., Lambers, L., Ehrig, H., Orejas, F.: Attributed graph transformation with inheritance: efficient conflict detection and local confluence analysis using abstract critical pairs. TCS 424, 46–68 (2012).  https://doi.org/10.1016/j.tcs.2012.01.032 MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Habel, A., Plump, D.: Relabelling in graph transformation. In: Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2002. LNCS, vol. 2505, pp. 135–147. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-45832-8_12 CrossRefGoogle Scholar
  9. 9.
    Habel, A., Plump, D.: \(\cal{M}, \cal{N}\)-adhesive transformation systems. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2012. LNCS, vol. 7562, pp. 218–233. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-33654-6_15 CrossRefGoogle Scholar
  10. 10.
    Heckel, R., Küster, J.M., Taentzer, G.: Confluence of typed attributed graph transformation systems. In: Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2002. LNCS, vol. 2505, pp. 161–176. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-45832-8_14 CrossRefGoogle Scholar
  11. 11.
    Hristakiev, I., Plump, D.: A unification algorithm for GP 2. In: Graph Computation Models (GCM 2014), Revised Selected Papers. Electronic Communications of the EASST, vol. 71 (2015). http://journal.ub.tu-berlin.de/eceasst/article/view/1002,  https://doi.org/10.14279/tuj.eceasst.71.1002
  12. 12.
    Hristakiev, I., Plump, D.: Attributed graph transformation via rule schemata: Church-Rosser theorem. In: Milazzo, P., Varró, D., Wimmer, M. (eds.) STAF 2016 Collocated Workshops, Revised Selected Papers. LNCS, vol. 9946, pp. 145–160. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-50230-4_11 CrossRefGoogle Scholar
  13. 13.
    Hristakiev, I., Plump, D.: Towards critical pair analysis for the graph programming language GP 2 (long version) (2017). https://www.cs.york.ac.uk/plasma/publications/pdf/HristakievPlump.WADT16.Long.pdf
  14. 14.
    Kulcsár, G., Deckwerth, F., Lochau, M., Varró, G., Schürr, A.: Improved conflict detection for graph transformation with attributes. In: Proceedings of Graphs as Models, GaM 2015, EPTCS, vol. 181, pp. 97–112 (2015).  https://doi.org/10.4204/EPTCS.181.7
  15. 15.
    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 CrossRefGoogle Scholar
  16. 16.
    Plump, D.: The design of GP 2. In: Proceedings of International Workshop on Reduction Strategies in Rewriting and Programming, WRS 2011, EPTCS, vol. 82, pp. 1–16 (2012).  https://doi.org/10.4204/EPTCS.82.1

Copyright information

© IFIP International Federation for Information Processing 2017

Authors and Affiliations

  1. 1.University of YorkYorkUK

Personalised recommendations