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Rewriting as a Special Case of Noncommutative Groebner Basis Theory

Anne Heyworth
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Abstract

Rewriting for semigroups is a special case of Groebner basis theory for noncommutative polynomial algebras. The fact is a kind of folklore but is not fully recognised. The aim of this paper is to elucidate this relationship, showing that the noncommutative Buchberger algorithm corresponds step-by-step to the Knuth-Bendix completion procedure.

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Anne Heyworth. 1999-01-11. Rewriting as a Special Case of Noncommutative Groebner Basis Theory. https://arxiv.org/abs/math/9901044

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