## Section: New Results

### Graph Rewriting

Guillaume Bonfante and Bruno Guillaume studied formal properties of the Graph Rewriting in [12] . It is well-known that some linguistic phenomena do not cope properly with trees as the core mathematical structure to represent linguistic informations. In a former paper, the authors showed the benefit of encoding linguistic structures by graphs and of using graph rewriting rules to compute on those structures.

The Graph Rewriting formalism they consider is a formalization of the system which is implemented in the Grew software. Justified by some linguistic considerations, this Graph Rewriting formalization is characterized by two features: first, there is no node creation along computations and second, there are non-local edge modifications. Under these hypotheses, the article shows that uniform termination is undecidable and that non-uniform termination is decidable. Two termination techniques based on weights are described and a complexity bound on the derivation length for these rewriting systems is given.