THE REPLENISHMENT ALGORITHM IN ALGEBRAS 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 algeb...

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Bibliographic Details
Published in:Cybernetics and Systems Analysis 2021, Vol.57 (5), p.820
Main Authors: Lvov, M, Tarasich, Y
Format: Report
Language:English
Subjects:
Algebra
Algorithms
Analysis
Online Access:Get full text
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Summary: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.
ISSN:1060-0396
DOI:10.1007/s10559-021-00407-0