Polynomial Graph Parsing with Non-Structural Reentrancies

Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find a generative device that is sufficiently powerful to represent languages of semantic graphs, while at the same allowing efficient parsing. We add to this line of work by introducing graph extension grammar, which consists of an algebra over graphs together with a regular tree grammar that generates expressions over the operations of the algebra. Due to the design of the operations, these grammars can generate graphs with non-structural reentrancies; a type of node-sharing that is excessively common in formalisms such as abstract meaning representation, but for which existing devices offer little support. We provide a parsing algorithm for graph extension grammars, which is proved to be correct and run in polynomial time.