Computational Complexity of Probabilistic Disambiguation by means of Tree-Grammars

This paper studies the computational complexity of disambiguation under probabilistic tree-grammars and context-free grammars. It presents a proof that the following problems are NP-hard: computing the Most Probable Parse (MPP) from a sentence or from a word-graph, and computing the Most Probable Sentence (MPS) from a word-graph. The NP-hardness of computing the MPS from a word-graph also holds for Stochastic Context-Free Grammars. Consequently, the existence of deterministic polynomial-time algorithms for solving these disambiguation problems is a highly improbable event.