Synchronous forest substitution grammars

The expressive power of synchronous forest (tree-sequence) substitution grammars (SFSGs) is studied in relation to multi bottom-up tree transducers (MBOTs). It is proved that SFSGs have exactly the same expressive power as compositions of an inverse MBOT with an MBOT. This result is used to derive complexity results for SFSGs and the fact that compositions of an MBOT with an inverse MBOT can compute tree translations that cannot be computed by any SFSG, although the class of tree translations computable by MBOTs is closed under composition

Multiple Context-Free Tree Grammars: Lexicalization and Characterization

Multiple (simple) context-free tree grammars are investigated, where "simple" means "linear and nondeleting". Every multiple context-free tree grammar that is finitely ambiguous can be lexicalized; i.e., it can be transformed into an equivalent one (generating the same tree language) in which each rule of the grammar contains a lexical symbol. Due to this transformation, the rank of the nonterminals increases at most by 1, and the multiplicity (or fan-out) of the grammar increases at most by the maximal rank of the lexical symbols; in particular, the multiplicity does not increase when all lexical symbols have rank 0. Multiple context-free tree grammars have the same tree generating power as multi-component tree adjoining grammars (provided the latter can use a root-marker). Moreover, every multi-component tree adjoining grammar that is finitely ambiguous can be lexicalized. Multiple context-free tree grammars have the same string generating power as multiple context-free (string) grammars and polynomial time parsing algorithms. A tree language can be generated by a multiple context-free tree grammar if and only if it is the image of a regular tree language under a deterministic finite-copying macro tree transducer. Multiple context-free tree grammars can be used as a synchronous translation device.Comment: 78 pages, 13 figure

Algebraic decoder specification: coupling formal-language theory and statistical machine translation: Algebraic decoder specification: coupling formal-language theory and statistical machine translation

The specification of a decoder, i.e., a program that translates sentences from one natural language into another, is an intricate process, driven by the application and lacking a canonical methodology. The practical nature of decoder development inhibits the transfer of knowledge between theory and application, which is unfortunate because many contemporary decoders are in fact related to formal-language theory. This thesis proposes an algebraic framework where a decoder is specified by an expression built from a fixed set of operations. As yet, this framework accommodates contemporary syntax-based decoders, it spans two levels of abstraction, and, primarily, it encourages mutual stimulation between the theory of weighted tree automata and the application

Synchronous Forest Substitution Grammars

Abstract. The expressive power of synchronous forest (tree-sequence) substitution grammars (SFSG) is studied in relation to multi bottom-up tree transducers (MBOT). It is proved that SFSG have exactly the same expressive power as compositions of an inverse MBOT with an MBOT. This result is used to derive complexity results for SFSG and the fact that compositions of an MBOT with an inverse MBOT can compute tree translations that cannot be computed by any SFSG, although the class of tree translations computable by MBOT is closed under composition.