Knuth–Bendix completion algorithm

The Knuth–Bendix completion algorithm (named after Donald Knuth and Peter Bendix) is a semi-decision algorithm for transforming a set of equations (over terms) into a confluent term rewriting system. When the algorithm succeeds, it effectively solves the word problem for the specified algebra. Buchberger's algorithm for computing Gröbner bases is a very similar algorithm. Although developed independently, it may also be seen as the instantiation of Knuth–Bendix algorithm in the theory of polynomial rings.

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enThe Knuth–Bendix completion algorithm (named after Donald Knuth and Peter Bendix) is a semi-decision algorithm for transforming a set of equations (over terms) into a confluent term rewriting system. When the algorithm succeeds, it effectively solves the word problem for the specified algebra. Buchberger's algorithm for computing Gröbner bases is a very similar algorithm. Although developed independently, it may also be seen as the instantiation of Knuth–Bendix algorithm in the theory of polynomial rings.
Has abstract
enThe Knuth–Bendix completion algorithm (named after Donald Knuth and Peter Bendix) is a semi-decision algorithm for transforming a set of equations (over terms) into a confluent term rewriting system. When the algorithm succeeds, it effectively solves the word problem for the specified algebra. Buchberger's algorithm for computing Gröbner bases is a very similar algorithm. Although developed independently, it may also be seen as the instantiation of Knuth–Bendix algorithm in the theory of polynomial rings.
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Algorithm
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Knuth–Bendix completion algorithm
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enKnuth–Bendix completion algorithm
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www.cs.tufts.edu/~nr/cs257/archive/don-knuth/knuth-bendix.pdf
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Algebra
Algorithm
Binary relation
Buchberger's algorithm
Category:Combinatorics on words
Category:Computational group theory
Category:Donald Knuth
Category:Rewriting systems
Computational group theory
Confluence (abstract rewriting)
Confluence (term rewriting)
Convergent term rewrite system
Converse relation
Coset
Critical pair (logic)
Critical pair lemma
Donald E. Knuth
Encompassment ordering
Equation
Equivalence closure
E theorem prover
Finitely presented group
Finitely presented monoid
Free Abelian group
Generating set of a group
Gröbner basis
Ground confluent
Group (mathematics)
Logged rewriting
Newman's lemma
Normal form (term rewriting)
Polynomial ring
Presentation of a group
Reduction ordering
Reflexive transitive closure
Relation (mathematics)
Relation composition
Resolution (logic)
Rewrite closure
Semi-algorithm
Semidecidable
Shortlex order
Term (logic)
Term rewriting system
Variant (logic)
Well-ordered
Word problem (mathematics)
SameAs
2e2w7
Complétion de Knuth-Bendix
m.02wqch
Q2835803
クヌース・ベンディックス完備化アルゴリズム
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Category:Combinatorics on words
Category:Computational group theory
Category:Donald Knuth
Category:Rewriting systems
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enKnuth–Bendix Completion Algorithm
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enKnuth-BendixCompletionAlgorithm
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