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Automates finis et ensembles normaux

Christian Mauduit (1986)

Annales de l'institut Fourier

Soit u = ( u n ) n ∈ N une suite strictement croissante d’entiers reconnaissable par un automate fini. Nous montrons qu’une condition nécessaire et suffisante pour que l’ensemble normal associé a u soit exactement R ∖ Q est que l’un au moins des sommets qui reconnaît la suite u soit précédé dans le graphe de l’automate par un sommet possédant au moins deux circuits fermés distincts. Cette condition peut se traduire quantitativement en disant que la suite u doit être plus “dense” que toute suite exponentielle.

Automatic differentiation and its program realization

Jan Hartman, Ladislav Lukšan, Jan Zítko (2009)

Kybernetika

Automatic differentiation is an effective method for evaluating derivatives of function, which is defined by a formula or a program. Program for evaluating of value of function is by automatic differentiation modified to program, which also evaluates values of derivatives. Computed values are exact up to computer precision and their evaluation is very quick. In this article, we describe a program realization of automatic differentiation. This implementation is prepared in the system UFO, but its...

Automatic differentiation platform : design

Christèle Faure (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Automatic differentiation (AD) has proven its interest in many fields of applied mathematics, but it is still not widely used. Furthermore, existing numerical methods have been developed under the hypotheses that computing program derivatives is not affordable for real size problems. Exact derivatives have therefore been avoided, or replaced by approximations computed by divided differences. The hypotheses is no longer true due to the maturity of AD added to the quick evolution of machine capacity....

Automatic Differentiation Platform: Design

Christèle Faure (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Automatic differentiation (AD) has proven its interest in many fields of applied mathematics, but it is still not widely used. Furthermore, existing numerical methods have been developed under the hypotheses that computing program derivatives is not affordable for real size problems. Exact derivatives have therefore been avoided, or replaced by approximations computed by divided differences. The hypotheses is no longer true due to the maturity of AD added to the quick evolution of machine capacity....

Automatic Identification of False Friends in Parallel Corpora: Statistical and Semantic Approach

Nakov, Svetlin (2009)

Serdica Journal of Computing

False friends are pairs of words in two languages that are perceived as similar but have different meanings. We present an improved algorithm for acquiring false friends from sentence-level aligned parallel corpus based on statistical observations of words occurrences and co-occurrences in the parallel sentences. The results are compared with an entirely semantic measure for cross-lingual similarity between words based on using the Web as a corpus through analyzing the words’ local contexts extracted...

Automaticity IV : sequences, sets, and diversity

Jeffrey Shallit (1996)

Journal de théorie des nombres de Bordeaux

This paper studies the descriptional complexity of (i) sequences over a finite alphabet ; and (ii) subsets of N (the natural numbers). If ( s ( i ) ) i ≥ 0 is a sequence over a finite alphabet Δ , then we define the k -automaticity of s , A s k ( n ) , to be the smallest possible number of states in any deterministic finite automaton that, for all i with 0 ≤ i ≤ n , takes i expressed in base k as input and computes s ( i ) . We give examples of sequences that have high automaticity in all bases k ; for example, we show that the characteristic...

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