Abstract
We introduce two techniques for proving termination of graph transformation systems. We do not fix a single initial graph, but consider arbitrary initial graphs (uniform termination), but also certain sets of initial graphs (non-uniform termination). The first technique, which can also be used to show non-uniform termination, uses a weighted type graph to assign weights to graphs. The second technique reduces uniform termination of graph transformation systems of a specific form to uniform termination of cycle rewriting, a variant of string rewriting.
Chapter PDF
References
Aßmann, U.: Graph rewrite systems for program optimization. ACM Transactions on Programming Languages and Systems 22(4), 583–637 (2000)
Bottoni, P., Hoffman, K., Presicce, F.P., Taentzer, G.: High-level replacement units and their termination properties. Journal of Visual Languages and Computing (2005)
Bruggink, H.J.S.: Towards a systematic method for proving termination of graph transformation systems. In: Proceedings of GT-VC 2007 (2007)
Corradini, A., Montanari, U., Rossi, F.: Graph processes. Fundamenta Informaticae 26(3/4), 241–265 (1996)
Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Algebraic approaches to graph transformation I: Basic concepts and double pushout approach. In: Rozenberg, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation. Foundations, vol. 1, World Scientific (1997)
Ehrig, H., Ehrig, K., de Lara, J., Taentzer, G., Varró, D., Varró-Gyapay, S.: Termination criteria for model transformation. In: Cerioli, M. (ed.) FASE 2005. LNCS, vol. 3442, pp. 49–63. Springer, Heidelberg (2005)
Geser, A., Hofbauer, D., Waldmann, J.: Match-bounded string rewriting. Applicable Algebra in Engineering, Communication and Computing 15(3-4), 149–171 (2004)
Koprowski, A., Waldmann, J.: Arctic termination ... Below zero. In: Voronkov, A. (ed.) RTA 2008. LNCS, vol. 5117, pp. 202–216. Springer, Heidelberg (2008)
Plump, D.: Termination of graph rewriting is undecidable. Fundementa Informaticae 33(2), 201–209 (1998)
Varró, D., Varró–Gyapay, S., Ehrig, H., Prange, U., Taentzer, G.: Termination analysis of model transformations by petri nets. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 260–274. Springer, Heidelberg (2006)
Zantema, H.: Termination of term rewriting by semantic labelling. Fundementa Informaticae 24, 89–105 (1995)
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, Heidelberg (2014)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 IFIP International Federation for Information Processing
About this paper
Cite this paper
Bruggink, H.J.S., König, B., Zantema, H. (2014). Termination Analysis for Graph Transformation Systems. In: Diaz, J., Lanese, I., Sangiorgi, D. (eds) Theoretical Computer Science. TCS 2014. Lecture Notes in Computer Science, vol 8705. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44602-7_15
Download citation
DOI: https://doi.org/10.1007/978-3-662-44602-7_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44601-0
Online ISBN: 978-3-662-44602-7
eBook Packages: Computer ScienceComputer Science (R0)