On the Expressivity of Linear Transductions

We investigate the formal expressivity properties of linear transductions, the class of transductions generated by linear transduction grammars, linear inversion transduction grammars and preterminalized linear inversion transduction grammars. While empirical results such as those in previous work are of course an ultimate test of modeling adequacy for machine translation applications, it is equally important to understand the formal theoretical properties of any such new representation. An important part of the expressivity of a transduction is the possibility to align tokens between the two languages generated. We refer to the number of different alignments that are allowed under a transduction as its weak alignment capacity. This aspect of expressivity is quantified for linear transductions using preterminalized linear inversion transduction grammars, and compared to the expressivity of finite-state transductions, inversion transductions and syntax-directed transductions.