Proving Termination of Graph Transformation Systems using Weighted Type Graphs over Semirings
Logic in Computer Science
2023-10-12 v3 Formal Languages and Automata Theory
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 is inspired by the tropical and arctic type graphs of [5] and introduces 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.
Keywords
Cite
@article{arxiv.1505.01695,
title = {Proving Termination of Graph Transformation Systems using Weighted Type Graphs over Semirings},
author = {H. J. Sander Bruggink and Barbara König and Dennis Nolte and Hans Zantema},
journal= {arXiv preprint arXiv:1505.01695},
year = {2023}
}