Proving Termination of Graph Transformation Systems using Weighted Type Graphs over Semirings

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...

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Bibliographic Details
Main Authors: Bruggink, H. J. Sander, König, Barbara, Nolte, Dennis, Zantema, Hans
Format: Report
Language:unknown
Published: arXiv 2015
Subjects:
Logic in Computer Science cs.LO
Formal Languages and Automata Theory cs.FL
FOS Computer and information sciences
Arctic
Online Access:https://dx.doi.org/10.48550/arxiv.1505.01695
https://arxiv.org/abs/1505.01695
Description
Summary: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 introduced in a previous paper 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.

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