Iteration of rational transductions

Iteration of rational transductions

The purpose of this paper is to show connections between iterated length preserving rational transductions and linear space computations Hence we study the smallest family of transductions containing length preserving rational transductions and closed under union composition and iteration We give several characterizations of this class using re stricted classes of length preserving rational tra...

Logical and Algebraic Characterizations of Rational Transductions

Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free automata, star-free expressions, aperiodic (finite) congruences, or first-order (FO) logic. In particular, their algebraic characterization by aperiodic con...

A rational QR-iteration

In this manuscript a new type of QR-iteration will be presented. Each step of this new iteration consists of two substeps. In the explicit version, first an RQ-factorization of the initial matrix A−κI = RQ will be computed, followed by a QR-factorization of the matrix (A−σI)QH . Applying the unitary similarity transformation defined by the QR-factorization of the transformed matrix (A−σI)QH , w...

Economy of Descriptions for Basic Constructions on Rational Transductions

Weighted Rational Transductions and their Application to Human Language Processing

We present the concepts of weighted language, ~ansduction and automaton from algebraic automata theory as a general framework for describing and implementing decoding cascades in speech and language processing. This generality allows us to represent uniformly such information sources as pronunciation dictionaries, language models artd lattices, and to use uniform algorithms for building decodin...