On the Complexity of ID/LP Parsing
Recent linguistic theories cast surface complexity as the result of interacting subsystems of constraints. For instance, the ID/LP grammar formalism separates constraints on immediate dominance from those on linear order. Shieber (1983) has shown how to carry out direct parsing of ID/LP grammars. His algorithm uses ID and LP constraints directly in language processing, without expanding them into a context-free "object grammar." This report examines the computational difficulty of ID/LP parsing. Shieber's purported O (G square times n cubed) runtime bound underestimated the difficulty of ID/LP parsing; the worst-case runtime of his algorithm is exponential in size. A reduction of the vertex-cover problem proves that ID/LP parsing is NP-complete. The growth of the internal data structures is the source of difficulty in Shieber's algorithm. The computational and linguistic implications of these results are discussed. Despite the potential for combinatorial explosion, Shieber's algorithm remains better than the alternative of parsing an expanded object grammar.