On the String Translations Produced by Multi Bottom-Up Tree Transducers

Many current approaches to syntax-based statistical machine translation fall under the theoretical framework of synchronous tree substitution grammars (STSGs). Tree substitution grammars (TSGs) generalize context-free grammars (CFGs) in that each rule expands a nonterminal to produce an arbitrarily large tree fragment, rather than a fragment of depth one as in a CFG. Synchronous TSGs generate tree fragments in the source and target languages in parallel, with each rule producing a tree fragment in either language. Systems such as that of Galley et al. (2006) extract STSG rules from parallel bilingual text that has been automatically parsed in one language, and the STSG nonterminals correspond to nonterminals in these parse trees. Chiang’s (2007) Hiero system produces simpler STSGs with a single nonterminal. STSGs have the advantage that they can naturally express many re-ordering and restructuring operations necessary for machine translation (MT). They have the disadvantage, however, that they are not closed under composition (Maletti et al. 2009). Therefore, if one wishes to construct anMT system as a pipeline of STSG operations, the result may not be expressible as an STSG. Recently, Maletti (2010) has argued that multi bottom–up tree transducers (MBOTs) (Lilin 1981; Arnold and Dauchet 1982; Engelfriet, Lilin, and Maletti 2009) provide a useful representation for natural language processing applications because they generalize STSGs, but have the added advantage of being closed under composition. MBOTs generalize traditional bottom–up tree transducers in that they allow transducer states to pass more than one output subtree up to subsequent transducer operations. The number of subtrees taken by a state is called its rank. MBOTs are linear and non-deleting; that is, operations cannot copy or delete arbitrarily large tree fragments. Although STSGs and MBOTs both perform operations on trees, it is important to note that, in MT, we are primarily interested in translational relations between strings. Tree operations such as those provided by STSGs are ultimately tools to translate a string