Proving termination of graph transformation systems using weighted type graphs over semirings

H.J.S. Bruggink, B. König, D. Nolte, H. Zantema

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3 Downloads (Pure)

Abstract

We introduce techniques for proving uniform termination of graph transformation systems, based on matrix interpretations for string rewriting. We generalize this technique by adapting it to graph rewriting instead of string rewriting and by generalizing to ordered semirings. In this way we obtain a framework which includes the tropical and arctic type graphs of [6] and a new variant of arithmetic type graphs. These type graphs can be used to assign weights to graphs and to show that these weights decrease in every rewriting step in order to prove termination. We present an example involving counters and discuss the implementation in the tool Grez.
Original languageEnglish
Title of host publicationGraph Transformation (8th International Conference, ICGT 2015, Held as Part of STAF 2015, L'Aquila, Italy, July 21-23, 2015. Proceedings)
EditorsF. Parisi-Presicce, B. Westfechtel
Place of PublicationCham
PublisherSpringer
Pages52-68
ISBN (Print)978-3-319-21144-2
DOIs
Publication statusPublished - 2015

Publication series

NameLecture Notes in Computer Science
Volume9151
ISSN (Print)0302-9743

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    Bruggink, H. J. S., König, B., Nolte, D., & Zantema, H. (2015). Proving termination of graph transformation systems using weighted type graphs over semirings. In F. Parisi-Presicce, & B. Westfechtel (Eds.), Graph Transformation (8th International Conference, ICGT 2015, Held as Part of STAF 2015, L'Aquila, Italy, July 21-23, 2015. Proceedings) (pp. 52-68). (Lecture Notes in Computer Science; Vol. 9151). Cham: Springer. https://doi.org/10.1007/978-3-319-21145-9_4