Synchronous context-free grammars (SynCFG or SCFG; not to be confused with stochastic CFGs

Stochastic context-free grammar

A stochastic context-free grammar is a context-free grammar in which each production is augmented with a probability...

 constitute a formal model of natural language

Natural language

In the philosophy of language, a natural language is any language which arises in an unpremeditated fashion as the result of the innate facility for language possessed by the human intellect. A natural language is typically used for communication, and may be spoken, signed, or written...

 syntax

Syntax

In linguistics, syntax is the study of the principles and rules for constructing phrases and sentences in natural languages....

, developed in the area of statistical machine translation

Statistical machine translation

Statistical machine translation is a machine translation paradigm where translations are generated on the basis of statistical models whose parameters are derived from the analysis of bilingual text corpora...

 (MT).

The theory of SynCFGs borrows from syntax-directed transduction and syntax-based machine translation, modeling the reordering of clauses that occurs when translating a sentence by correspondences between phrase-structure rules in the source and target languages. Performance of SCFG-based MT systems has been found comparable with, or even better than, state-of-the-art phrase-based machine translation systems.
Several algorithms exist to perform translation using SynCFGs.

Formalism

Rules in a SynCFG are superficially similar to CFG rules, except that they specify the structure of two phrases at the same time; one in the source language (the language being translated) and one in the target language. Numeric indices indicate correspondences between non-terminals in both constituent trees. Chiang gives the Chinese/English example:

(yu you , have with )