... probability of generating all spansother than a k, as in A* search for CFGs (Klein and Manning, 2003), and tic-tac-toe pruning for word-based ITGs (Zhang and Gildea, 2005). As the cal-culation of the ... probabilities are calcu-lated for e and f independently, and can be calcu-lated in n2time by processing each α in ascendingorder, and each β in descending order in a fashionsimilar to that of the ... Neubig1,2, Taro Watanabe2, Shinsuke Mori1, Tatsuya Kawahara11Graduate School of Informatics, Kyoto UniversityYoshida Honmachi, Sakyo-ku, Kyoto, Japan2National Institute of Information and Communication...