We present a formal framework that generalizes a variety of monolingual and synchronous grammar formalisms for parsing and translation. Our framework is based on regular tree grammars that describe derivation trees, which are interpreted in arbitrary algebras. We obtain generic parsing algorithms by exploiting closure properties of regular tree languages.

Hierarchical-phrase based machine translation model is a popular translation model which combines advantages of phrase-based translation models and syntax-based translation models. However, since there are no linguistic constraints in the procedure of current hierarchical phrase extraction, there are a large number of redundant generalized rules extracted. In this paper, we propose two strategi...

We introduce a novel framework for the expression, rapid-prototyping, and evaluation of statistical machine-translation (MT) systems using graphical models. The framework extends dynamic Bayesian networks with multiple connected different-length streams, switching variable existence and dependence mechanisms, and constraint factors. We have implemented a new general-purpose MT training/decoding...

Generalized n-gons were introduced by Tits in a famous work on triality [20] of 1959, in order to propose an axiomatic and combinatorial treatment for semisimple algebraic groups (including Chevalley groups and groups of Lie type) of relative rank 2. They are the central rank 2 incidence geometries, and the atoms of the more general “Tits-buildings.” If the number of elements of a generalized n...

This paper studies a suitably normalized set of generalized Hermite polynomials and sets down a relevant Mehler formula, Rodrigues formula, and generalized translation operator. Weighted generalized Hermite polynomials are the eigenfunctions of a generalized Fourier transform which satisfies an F. and M. Riesz theorem on the absolute continuity of analytic measures. The Bose-like oscillator cal...

This paper describes a generalized translation memory system, which takes advantage of sentence level matching, sub-sentential matching, and pattern-based machine translation technologies. All of the three techniques generate translation suggestions with the assistance of word alignment information. For the sentence level matching, the system generates the translation suggestion by modifying th...

Some estimates are proved for the generalized Fourier-Bessel transform in the space (L^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

We review some aspects of our recent work on the approximation of functions by neural and generalized translation networks.