Graphs have a variety of uses in natural language processing, particularly as representations of linguistic meaning. A deficit in this area of research is a formal framework for creating, combining, and using models involving graphs that parallels the frameworks of finite automata for strings and finite tree automata for trees. A possible starting point for such a framework is the formalism of directed acyclic graph (DAG) automata, defined by Kamimura and Slutzki and extended by Quernheim and Knight. In this article, we study the latter in depth, demonstrating several new results, including a practical recognition algorithm that can be used for inference and learning with models defined on DAG automata. We also propose an extension to graphs with unbounded node degree and show that our results carry over to the extended formalism.

We present a statistical machine translation model that uses hierarchical phrases —phrases that contain subphrases. The model is formally a synchronous context-free grammar but is learned from a parallel text without any syntactic annotations. Thus it can be seen as combining fundamental ideas from both syntax-based translation and phrase-based translation. We describe our system's training and decoding methods in detail, and evaluate it for translation speed and translation accuracy. Using BLEU as a metric of translation accuracy, we find that our system performs significantly better than the Alignment Template System, a state-of-the-art phrase-based system.