Uniform vs. Nonuniform Membership for Mildly Context-Sensitive Languages: A Brief Survey

Parsing for mildly context-sensitive language formalisms is an important area within natural language processing. While the complexity of the parsing problem for some such formalisms is known to be polynomial, this is not the case for all of them. This article presents a series of results regarding the complexity of parsing for linear context-free rewriting systems and deterministic tree-walking transducers. We discuss the difference between uniform and nonuniform complexity measures and how parameterized complexity theory can be used to investigate how different aspects of the formalisms influence how hard the parsing problem is. The main results we survey are all hardness results and indicate that parsing is hard even for relatively small values of parameters such as rank and fan-out in a rewriting system.