Permutations via linear translators

International audienceWe show that many infinite classes of permutations over finite fields can be constructedvia translators with a large choice of parameters. We first characterize some functionshaving linear translators, based on which several families of permutations are then derived. Extending the results of \cite{kyu}, we give in several cases thecompositional inverse of these permutations. The connection with complete permutations is also utilized to provide further infinite classes of permutations. Moreover, wepropose new tools to study permutations of the form $x\mapsto x+(x^{p^m}-x+\delta)^s$ and a few infinite classes of permutations of this form are proposed

A Survey of Word Reordering in Statistical Machine Translation: Computational Models and Language Phenomena

Word reordering is one of the most difficult aspects of statistical machine translation (SMT), and an important factor of its quality and efficiency. Despite the vast amount of research published to date, the interest of the community in this problem has not decreased, and no single method appears to be strongly dominant across language pairs. Instead, the choice of the optimal approach for a new translation task still seems to be mostly driven by empirical trials. To orientate the reader in this vast and complex research area, we present a comprehensive survey of word reordering viewed as a statistical modeling challenge and as a natural language phenomenon. The survey describes in detail how word reordering is modeled within different string-based and tree-based SMT frameworks and as a stand-alone task, including systematic overviews of the literature in advanced reordering modeling. We then question why some approaches are more successful than others in different language pairs. We argue that, besides measuring the amount of reordering, it is important to understand which kinds of reordering occur in a given language pair. To this end, we conduct a qualitative analysis of word reordering phenomena in a diverse sample of language pairs, based on a large collection of linguistic knowledge. Empirical results in the SMT literature are shown to support the hypothesis that a few linguistic facts can be very useful to anticipate the reordering characteristics of a language pair and to select the SMT framework that best suits them.Comment: 44 pages, to appear in Computational Linguistic

Further Results on Permutation Polynomials over Finite Fields

Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a demonstration of the theorems, we present a number of classes of explicit permutation polynomials on \gf_q