Automates topologiques et ensembles reconnaissables
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 (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 (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....
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...
This paper studies the descriptional complexity of (i) sequences over a finite alphabet ; and (ii) subsets of (the natural numbers). If is a sequence over a finite alphabet , then we define the -automaticity of , to be the smallest possible number of states in any deterministic finite automaton that, for all with , takes expressed in base as input and computes . We give examples of sequences that have high automaticity in all bases ; for example, we show that the characteristic...
The main objective of the polynomial approximation is the development of polynomial time algorithms for NP-hard problems, these algorithms guaranteeing feasible solutions lying “as near as possible” to the optimal ones. This work is the fist part of a couple of papers where we introduce the key-concepts of the polynomial approximation and present the main lines of a new formalism. Our purposes are, on the one hand, to present this theory and its objectives and, on the other hand, to discuss the...