Abstract
We deduce the law of nonstationary recursion which makes it possible, for given a primitive set A = {a 1,...,a k }, k > 2, to construct an algorithm for finding the set of the numbers outside the additive semigroup generated by A. In particular, we obtain a new algorithm for determining the Frobenius numbers g(a 1,...,a k ). The computational complexity of these algorithms is estimated in terms of bit operations. We propose a two-stage reduction of the original primitive set to an equivalent primitive set that enables us to improve complexity estimates in the cases when the two-stage reduction leads to a substantial reduction of the order of the initial set.
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Original Russian Text © V.M. Fomichev, 2017, published in Diskretnyi Analiz i Issledovanie Operatsii, 2017, Vol. 24, No. 3, pp. 104–124.
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Fomichev, V.M. Computational complexity of the original and extended diophantine Frobenius problem. J. Appl. Ind. Math. 11, 334–346 (2017). https://doi.org/10.1134/S1990478917030048
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DOI: https://doi.org/10.1134/S1990478917030048