Bettina Just

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A vector m = (mx , ... , mn) eZ"\ {0} is called an integer relation for the real numbers a,, ... , an , if X)0,"1, = 0 holds. We present an algorithm that, when given algebraic numbers ax , ... , an and a parametere , either finds an integer relation for a,,... , an or proves that no relation of Euclidean length shorter than 1/e exists. Each algebraic(More)
Up to now, few models of computation with the power of evaluating discon-tinuous functions have been analyzed and few of their lower bounds or results on the decidability of languages are known. In this paper, we present a model of an " analytic computation tree " (ACT). These trees operate on real numbers and are able to compare real numbers, to evaluate(More)
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