Between a Rock and a Hard Place – Parsing for Hyperege Replacement DAG Grammars

We study the uniform membership problem for hyperedgereplacement grammars that generate directed acyclic graphs. The study of this type of language is motivated by applications in natural language processing. Our major result is a low-degree polynomial-time algorithm that solves the uniform membership problem for a restricted type of such grammars. We motivate the necessity of the restrictions by two different NP-completeness results.