Checking Bisimilarity for Attributed Graph Transformation

• Fernando Orejas
• Artur Boronat
• Ulrike Golas
• Nikos Mylonakis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7794)

Abstract

Borrowed context graph transformation is a technique developed by Ehrig and Koenig to define bisimilarity congruences from reduction semantics defined by graph transformation. This means that, for instance, this technique can be used for defining bisimilarity congruences for process calculi whose operational semantics can be defined by graph transformation. Moreover, given a set of graph transformation rules, the technique can be used for checking bisimilarity of two given graphs. Unfortunately, we can not use this ideas to check if attributed graphs are bisimilar, i.e. graphs whose nodes or edges are labelled with values from some given data algebra and where graph transformation involves computation on that algebra. The problem is that, in the case of attributed graphs, borrowed context transformation may be infinitely branching. In this paper, based on borrowed context transformation of what we call symbolic graphs, we present a sound and relatively complete inference system for checking bisimilarity of attributed graphs. In particular, this means that, if using our inference system we are able to prove that two graphs are bisimilar then they are indeed bisimilar. Conversely, two graphs are not bisimilar if and only if we can find a proof saying so, provided that we are able to prove some formulas over the given data algebra. Moreover, since the proof system is complex to use, we also present a tableau method based on the inference system that is also sound and relatively complete.

Keywords

Attributed graph transformation symbolic graph transformation borrowed contexts bisimilarity

References

1. 1.
Bonchi, F., Gadducci, F., König, B.: Synthesising CCS bisimulation using graph rewriting. Inf. Comput. 207(1), 14–40 (2009)
2. 2.
Bonchi, F., Gadducci, F., Monreale, G.V.: Labelled transitions for mobile ambients (as synthesized via a graphical encoding). Electr. Notes Theor. Comput. Sci. 242(1), 73–98 (2009)
3. 3.
Christensen, S., Hirshfeld, Y., Moller, F.: Bisimulation Equivalence is Decidable for Basic Parallel Processes. In: Best, E. (ed.) CONCUR 1993. LNCS, vol. 715, pp. 143–157. Springer, Heidelberg (1993)
4. 4.
Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. In: EATCS Monographs of Theoretical Comp. Sc. Springer (2006)Google Scholar
5. 5.
Ehrig, H., Golas, U., Habel, A., Lambers, L., Orejas, F.: M-adhesive transformation systems with nested application conditions. part 1. Math. Struct. in Com. Sc. (2012) (to appear)Google Scholar
6. 6.
Ehrig, H., König, B.: Deriving bisimulation congruences in the DPO approach to graph rewriting with borrowed contexts. Math. Struct. in Com. Sc. 16(6), 1133–1163 (2006)
7. 7.
Gadducci, F.: Graph rewriting for the pi-calculus. Math. Struct. in Com. Sc. 17(3), 407–437 (2007)
8. 8.
Giese, M., Hähnle, R.: Tableaux + constraints. In: TABLEAUX 2003 position paper (2003)Google Scholar
9. 9.
Hennessy, M., Lin, H.: Symbolic bisimulations. Theor. Comput. Sci. 138(2), 353–389 (1995)
10. 10.
Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. J. ACM 32(1), 137–161 (1985)
11. 11.
Hülsbusch, M., König, B.: Deriving Bisimulation Congruences for Conditional Reactive Systems. In: Birkedal, L. (ed.) FOSSACS 2012. LNCS, vol. 7213, pp. 361–375. Springer, Heidelberg (2012)
12. 12.
Jaffar, J., Maher, M., Marriot, K., Stuckey, P.: The semantics of constraint logic programs. The Journal of Logic Programming 37, 1–46 (1998)
13. 13.
Lack, S., Sobocinski, P.: Adhesive and quasiadhesive categories. Theor. Inf. App. 39, 511–545 (2005)
14. 14.
Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes, I and II. Inf. Comput. 100(1), 1–77 (1992)
15. 15.
Orejas, F., Boronat, A., Mylonakis, N.: Borrowed Contexts for Attributed Graphs. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2012. LNCS, vol. 7562, pp. 126–140. Springer, Heidelberg (2012)
16. 16.
Orejas, F., Lambers, L.: Symbolic attributed graphs for attributed graph transformation. ECEASST 30 (2010)Google Scholar
17. 17.
Orejas, F., Lambers, L.: Lazy graph transformation. Fund. Inf. 118, 65–96 (2012)
18. 18.
Park, D.: Concurrency and Automata on Infinite Sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981)
19. 19.
Rangel, G., König, B., Ehrig, H.: Bisimulation verification for the DPO approach with borrowed contexts. ECEASST 6 (2007)Google Scholar
20. 20.
Sangiorgi, D.: On the Proof Method for Bisimulation. In: Hájek, P., Wiedermann, J. (eds.) MFCS 1995. LNCS, vol. 969, pp. 479–488. Springer, Heidelberg (1995)
21. 21.
Sangiorgi, D.: A theory of bisimulation for the pi-calculus. Acta Inf. 33(1), 69–97 (1996)

Authors and Affiliations

• Fernando Orejas
• 1
• Artur Boronat
• 1
• 2
• Ulrike Golas
• 3
• Nikos Mylonakis
• 1
1. 1.Universitat Politècnica de CatalunyaSpain
2. 2.University of LeicesterUK