Lvov M., Tarasich Y.
The replenishment algorithm in algebra of sets

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. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: constructive algebras of sets, replenishment algorithm, standard basis, Number theory, Abstract reduction, Constructive algebra of set, Elementary number theory, Multi-sets, Reduction systems, Replenishment algorithm, Semi-algebraic sets, Simple++, Standard basis, Algebra

Cite:
Lvov M., Tarasich Y. (2021). The replenishment algorithm in algebra of sets. Cybernetics and Systems Analysis, 57 (5), 168–174. doi: https://doi.org/10.1007/s10559-021-00407-0 http://jnas.nbuv.gov.ua/article/UJRN-0001268758 [In Ukrainian].