... generic addition and multiplication operation,⊕ and ⊗, and their identities 0 and 1. Multipli-cation and addition must be associative. Multi-plication must distribute over addition, and v ⊗ 09GoalJJ ... 2003), lexical translation models(Brown et al., 1993), and finite-state conditionalrandom fields (Sha and Pereira, 2003) exemplifythe former, and hierarchical phrase-based modelsthe latter (Chiang, ... 15 was used, and all decoders were configured to use cube prun-ing with a limit of 30 candidates at each node and no further pruning. All decoders produced a BLEUscore between 31.4 and 31.6 (small...