Non-simplifying Graph Rewriting Termination
This addresses a theoretical challenge in computational linguistics for researchers using graph-based representations, but it is incremental as it builds on prior work on graph rewriting.
The paper tackles the problem of termination for graph rewriting systems with no node creation and non-local edge modifications, showing that uniform termination is undecidable while non-uniform termination is decidable, and provides termination techniques with complexity bounds on derivation length.
So far, a very large amount of work in Natural Language Processing (NLP) rely on trees as the core mathematical structure to represent linguistic informations (e.g. in Chomsky's work). However, some linguistic phenomena do not cope properly with trees. In a former paper, we showed the benefit of encoding linguistic structures by graphs and of using graph rewriting rules to compute on those structures. Justified by some linguistic considerations, graph rewriting is characterized by two features: first, there is no node creation along computations and second, there are non-local edge modifications. Under these hypotheses, we show that uniform termination is undecidable and that non-uniform termination is decidable. We describe two termination techniques based on weights and we give complexity bound on the derivation length for these rewriting system.