Basic features and development of the critical-pair/completion procedure
Proc. of the first international conference on Rewriting techniques and applications
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
Term Reduction Systems and Algebraic Algorithms
GWAI '81 Proceedings of the German Workshop on Artificial Intelligence
A short survey on the state of the art in matching and unification problems
ACM SIGSAM Bulletin
Completion of integral polynomials by AC-term completion
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Abstract canonical presentations
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
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The Knuth-Bendix procedure for the completion of a rewrite rule system and the Buchberger algorithm for computing a Gröbner basis of a polynomial ideal are very similar in two respects: they both start with an arbitrary specification of an algebraic structure (axioms for an equational theory and a basis for a polynomial ideal, respectively) which is transformed to a very special specification of this algebraic structure (a complete rewrite rule system and a Gröbner basis of the polynomial ideal, respectively). This special specification allows to decide many problems concerning the given algebraic structure. Moreover, both algorithms achieve their goals by employing the same basic concepts: formation of critical pairs and completion.Although the two methods are obviously related, the exact nature of this relation remains to be clarified. Based on previous work we show how the Knuth-Bendix procedure and the Buchberger algorithm can be seen as special cases of a more general completion procedure.