The field of statistical machine translation has made tremendous progress due to the rise of statistical methods, making it possible to obtain a translation system automatically from a bilingual collection of text. Some approaches do not even need any kind of linguistic annotation, and can infer translation rules from raw, unannotated data. However, most state-of-the art systems do linguistic structure little justice, and moreover many approaches that have been put forward use ad-hoc formalisms and algorithms. This inevitably leads to duplication of effort, and a separation between theoretical researchers and practitioners. In order to remedy the lack of motivation and rigor, the contributions of this dissertation are threefold: 1. After laying out the historical background and context, as well as the mathematical and linguistic foundations, a rigorous algebraic model of machine translation is put forward. We use regular tree grammars and bimorphisms as the backbone, introducing a modular architecture that allows different input and output formalisms. 2. The challenges of implementing this bimorphism-based model in a machine translation toolkit are then described, explaining in detail the algorithms used for the core components. 3. Finally, experiments where the toolkit is applied on real-world data and used for diagnostic purposes are described. We discuss how we use exact decoding to reason about search errors and model errors in a popular machine translation toolkit, and we compare output formalisms of different generative capacity.

The field of statistical machine translation has made tremendous progress due to the rise of statistical methods, making it possible to obtain a translation system automatically from a bilingual collection of text. Some approaches do not even need any kind of linguistic annotation, and can infer translation rules from raw, unannotated data. However, most state-of-the art systems do linguistic structure little justice, and moreover many approaches that have been put forward use ad-hoc formalisms and algorithms. This inevitably leads to duplication of effort, and a separation between theoretical researchers and practitioners. In order to remedy the lack of motivation and rigor, the contributions of this dissertation are threefold: 1. After laying out the historical background and context, as well as the mathematical and linguistic foundations, a rigorous algebraic model of machine translation is put forward. We use regular tree grammars and bimorphisms as the backbone, introducing a modular architecture that allows different input and output formalisms. 2. The challenges of implementing this bimorphism-based model in a machine translation toolkit are then described, explaining in detail the algorithms used for the core components. 3. Finally, experiments where the toolkit is applied on real-world data and used for diagnostic purposes are described. We discuss how we use exact decoding to reason about search errors and model errors in a popular machine translation toolkit, and we compare output formalisms of different generative capacity.