Declarative Representation of Algorithms of Completion by Critical Pairs

A declarative representation of critical pairs for completion algorithms is described. The representation can be considered as a generic program that, after parametrization of some of its functions, realizes the Knuth-Bendix algorithm for solving the word problem in universal algebras or Buchberger...

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Bibliographic Details
Published in:Cybernetics and systems analysis Vol. 37; no. 6; pp. 795 - 799
Main Author: Volkov, V. A.
Format: Journal Article
Language:English
Published: New York Springer Nature B.V 01.11.2001
Subjects:
Algebra
Algorithms
Computer programming
Cybernetics
Logic programming
Mathematical models
Studies
ISSN:1060-0396, 1573-8337
Online Access:Get full text
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Summary:A declarative representation of critical pairs for completion algorithms is described. The representation can be considered as a generic program that, after parametrization of some of its functions, realizes the Knuth-Bendix algorithm for solving the word problem in universal algebras or Buchberger algorithm for constructing Grobner bases of polynomial ideals. The properties of termination and correction are considered. A realization of the representation in the APS algebraic system is described. [PUBLICATION ABSTRACT]
Bibliography:SourceType-Scholarly Journals-1
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ISSN:1060-0396
1573-8337
DOI:10.1023/A:1014569528986