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The Replenishment Algorithm in Algebras of Sets

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Abstract

The algorithm described can be called the replenishment algorithm by analogy with the Buchberger and Knuth–Bendix algorithms. Specific implementations of the theoretical construction (abstract reduction system) in algebras of finite, numerical, and linear semi-algebraic sets, as well as in the algebra of multisets are given. The elementary number theory problem interpreted as a problem of multiset algebra is considered. The main purpose of this study is to draw attention to simple examples of the replenishment algorithm application.

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Authors and Affiliations

  1. Kherson State University, Kherson, Ukraine

    M. Lvov & Y. Tarasich

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  1. M. Lvov
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  2. Y. Tarasich
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Correspondence to M. Lvov.

Additional information

Translated from Kibernetyka ta Systemnyi Analiz, No. 5, September–October, 2021, pp. 168–174.

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Lvov, M., Tarasich, Y. The Replenishment Algorithm in Algebras of Sets. Cybern Syst Anal 57, 820–826 (2021). https://doi.org/10.1007/s10559-021-00407-0

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  • DOI: https://doi.org/10.1007/s10559-021-00407-0

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