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On termination of Graph Rewriting Systems through language theory

Guillaume Bonfante 1 Miguel Couceiro 2
1 CARBONE - Carbone
LORIA - FM - Department of Formal Methods
2 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : The termination issue we tackle is rooted in natural language processing where graph rewriting systems (GRS) may contain a large number of rules, often in the order of thousands. Decidable concepts thus become mandatory to verify the termination of such systems. The notion of graph rewriting consider does not make any assumption on the structure of graphs (they are not “term graphs”, “port graphs” nor drags). The lack of algebraic structure in our setting led us to proposing two orders on graphs inspired from language theory: the matrix multiset-path order and the rational embedding order. We show that both are stable by context, which we then use to obtain the main contribution of the paper: under a suitable notion of “interpretation”, a GRS is terminating if and only if it is compatible with an interpretation.
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Contributor : Miguel Couceiro <>
Submitted on : Friday, February 14, 2020 - 9:45:04 AM
Last modification on : Tuesday, March 3, 2020 - 1:17:05 AM
Long-term archiving on: : Friday, May 15, 2020 - 12:44:22 PM


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  • HAL Id : hal-02478696, version 1


Guillaume Bonfante, Miguel Couceiro. On termination of Graph Rewriting Systems through language theory. 2020. ⟨hal-02478696⟩



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