Knuth Bendix completion algorithm

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	Donald Knuth - eBooks Encyclopedia
		Knuth published his first "scientific" article in a school magazine in 1957 under the title "Potrzebie System of Weights and Measures." In it, he defined the fundamental unit of length as the thickness of MAD magazine #26, and named the fundamental unit of force "whatmeworry".
		Knuth (pronounced "Ka-NOOTH" [1] (http://www-cs-faculty.stanford.edu/~knuth/faq.html)) is best known as the author of the multi-volume The Art of Computer Programming, one of the most highly respected references in the computer science field.
		In addition to his writings on computer science, Knuth is also the author of 3:16 Bible Texts Illuminated (1991), ISBN 0895792524, in which he attempts to examine the Bible by a process of stratified random sampling, namely an analysis of chapter 3, verse 16 of each book.
	www.ebooks.teleactivities.com /encyclopedia/index.php?title=Donald_Knuth (1099 words)

	Word problem for groups - Wikipedia, the free encyclopedia
		The related but different uniform word problem for finitely presented groups is the algorithmic problem of deciding, given as input a presentation for a group and two words in the generators, whether the words represent the same element in the group defined by the presentation.
		In abstract algebra, the word problem for a finitely generated group G is the algorithmic problem of deciding, given as input two words in the generators for G, whether they represent the same element of G.
		The word problem was one of the first examples of an unsolvable problem to be found not in mathematical logic or the theory of algorithms, but in one of the central branches of classical mathematics, algebra.
	en.wikipedia.org /wiki/Word_problem_for_groups (659 words)

	Citations: A Complete Proof of Correctness of the Knuth-Bendix Completion Algorithm - Huet (ResearchIndex)
		A complete proof of correctness of the knuth-bendix completion algorithm.
		A complete proof of correctness of the KnuthBendix completion algorithm.
		Huet, G., "A complete proof of correctness of the Knuth-Bendix completion procedure," JCSS 23, 1, 1981.
	citeseer.ist.psu.edu /context/276320/0 (481 words)

	seki.bib
		We develop algorithms to impose a hierarchical structure on proof protocols from completion based proof systems and to generate equational chains from them.
		Completion based proof methods are frequently regarded to have the disadvantage of being not goal oriented.
		The integration of this feature is based on the widespread assumption that, if equations are oriented by hand during completion and the completion process terminates with success, then the generated finite system is a maybe nonterminating but locally confluent system.
	www-ags.dfki.uni-sb.de /pub/bibsources/keller/seki.bib (11953 words)

	List of algorithms
		See also the list of data structures, list of algorithm general topics and list of terms relating to algorithms and data structures.
		Snapshot algorithm: a snapshot is the process of recording the global state of a system
		Rainflow-counting algorithm: Reduces a complex stress history to a count of elementary stress-reversals for use in fatigue analysis
	www.uncover.us /en/wikipedia/l/li/list_of_algorithms.html (779 words)

	Knuth
		After completion of his doctorate in 1963 Knuth became an Assistant Professor of Mathematics at the California Institute of Technology, being promoted to Associate Professor in 1966.
		One day when Knuth was meant to be performing with the College band he missed the bus taking the band to the performance so, finding himself with free time, he tried to solve a challenge problem that one of his mathematics professors had set.
		The problem was that Knuth did not believe in himself at this stage in his life and so his teachers doubted whether he had the personality, in particular the confidence, to succeed.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Knuth.html (2396 words)

	Creation of Automatic Groups and Arithmetic with Words
		The Knuth--Bendix completion procedure for monoids is now run on P to calculate the word difference arising from the generated equations thereby calculating the finite state automata associated with a short-lex automatic group.
		Note that the first time we run the AutomaticGroup function we are told that the Knuth-Bendix completion procedure did not complete fully (and hence the resulting automatic group is not confluent).
		Another point to be borne in mind is that the algorithms sometimes produce temporary disk files which the user does not normally see (because they are automatically removed after use), but can occasionally be very large.
	www.dtr.isy.liu.se /Magma/text369.html (1991 words)

	Automated Reasoning
		DPLL algorithms are made more efficient by strategies such as term indexing (ordering of the formula variables in an advantageous way), chronological backtracking (undoing work to a previous branching point if the process leads to a conflicting clause), and conflict-driven learning (determining the information to keep and where to backtrack).
		The Davis-Putnam-Logemann-Loveland (DPLL) algorithm was one of the first SAT search algorithms (Davis and Putnam 1960; Davis, Logemman and Loveland 1962) and is still considered one of the best complete SAT solvers; many of the complete SAT procedures in existence today can be considered optimizations and generalizations of DPLL.
		(Harrison 2001) discusses the verification of floating-point algorithms and the non-trivial mathematical properties that are proved by HOL under the guidance of the user.
	plato.stanford.edu /entries/reasoning-automated (12208 words)

	RTA open problem #35
		A complete proof of correctness of the Knuth-Bendix completion algorithm.
		] of the “completeness” of completion is predicated on the assumption that the ordering supplied to completion does not change during the process.
		Is there an example showing that completion is then incomplete (the persisting rules are not confluent)?
	www.lsv.ens-cachan.fr /rtaloop/problems/35.html (134 words)

	theorem_provers.doc
		If the universe is complete and decidable it is determined as well; free will can not exist; if on the other hand it is not complete and decidable free will can exist, but, of course, not everything can be proved.
		The search for completeness and decidability must be done but in the mean time, in order to solve problems (to make proofs) flexible and powerful programming systems are needed even if they do not have these two characteristics.
		It is complete when every known lemma can be proved.(Where the lemma has to be known sematically which is a matter of human interpretation.) It is decidable if the proof can be given.
	www.agfa.com /w3c/2002/02/thesis/theorem_provers.doc (5070 words)

	Formal grammar
		Though there is a tremendous body of literature on parsing algorithms, most of these algorithms assume that the language to be parsed is initially described by means of a generative formal grammar, and that the goal is to transform this generative grammar into a working parser.
		For example, for context-free grammars there are well-known algorithms to generate efficient LL parsers and LR parsers.
		An analytic grammar, in contrast, is a set of rules that assume an arbitrary string to be given as input, and which successively reduce or analyze that input string yield a final Boolean datatype, yes/no result indicating whether or not the input string is a member of the language described by the grammar.
	read-and-go.hopto.org /Formal-languages/Formal-grammar.html (1308 words)

	KnuthBendix.ma
		:[font = text; inactive; preserveAspect; ] This notebook implements Knuth-Bendix completion, as described in [5]; the algorithm used is basicly the one presented in [4].
		279-301 :[font = text; inactive; preserveAspect; ] [4] Huet, G., "A complete proof of correctness of the Knuth-Bendix completion algorithm", Journal of Computer and System Sciences, Vol.
		During the completion process it will therefore be necessary to simplify all the equations, and to remove the redundant ones.
	www.cs.cmu.edu /People/rvirga/mathematica/KnuthBendix.ma (1215 words)

	malbos02.html
		The resolution associated to the Knuth-Bendix completion algorithm, reflects the combinatorial properties of $\cc$.
		The purpose of this contribution is to generalize Kobayashi's theorem for monoids to ``monoids with several objects''.
		In particular, categories having finite complete presentations by graphs and relations have a Hochschild-Mitchell homology of finite type.
	www.di.ens.fr /~goubault/malbos02.html (105 words)

	MATHS: Mathematics
		Smith A 90, Alf Smith, The Knuth-Bendix Completion Algorithm and its Specification in Z, pp195-220 in Nicholls 90.
		Knuth and Bendix "Simple word problems in Universal Algebras" pp263-297 in Cl Probs in Abs Alg Leech 1970.
		There is no general algorithm for proving the equality of two formulae in a general logic with equality formulae [Post...].
	www.csci.csusb.edu /dick/maths/math_10_Intro.html (2114 words)

	Newsletter Dec 20, No. 9
		When a set of rules does not have the confluence property, it is augmented by new rules, using the so-called Knuth and Bendix completion algorithm, until the property becomes satisfied.
		This algorithm requires the set of rules to have the termination property, i.e., an expression cannot be rewritten forever.
		It has been proved that this algorithm allows one to perform as inductive proof without invoking explicitly an induction principle and to solve equations (unification) in the corresponding equational theory as well.
	www-csli.stanford.edu /Archive/calendar/1984-85/msg00010.html (980 words)

	Completion as a Derived Rule of Inference
		A simple first step in the investigation of term rewriting systems in higher order logic is to just insert the first order Knuth-Bendix completion algorithm unchanged into the more complicated logic.
		We present completion as a derived rule of inference, not (as usual) as an ad hoc procedure.
		The completion rule presented here is easily adaptable to other natural deduction logics with equality.
	www.cl.cam.ac.uk /~kxs/papers/kb.html (124 words)

	Sunroof bendix linkleri
		The Knuth-Bendix completion algorithm attempts to transform a finite set of...
		Knuth DE and Bendix PB "Simple Word Problems in Universal Algebra.
		Bendix washing machines, dryers and dishwashers are built to exacting European standards and every single one is expected to last as long as the models that...
	sunroof.linkleri.org /bendix.html (451 words)

	1
		The Knuth-Bendix completion algorithm attempts to transform a set of axioms into a canonical set of rewrite rules.
		Certain canonical sets are infinite, and in attempting to complete them, the algorithm never terminates.
		The importance of this property is that an algorithm that repeatedly applies rules to expressions wherever possible will always terminate, leaving the
	www.cse.iitb.ac.in /~kos/knuth-bendix.htm (1433 words)

	Abstracts
		This chapter is supposed to provide beginners in logic with the basics of term rewriting, the Knuth-Bendix completion algorithm and theorem proving by rewriting.
		Following early approaches by Wilhelm Ackermann a number of algorithms have been developed which accept a formula with predicate quantifiers as input and compute an equivalent first--order formula as output.
		In this chapter we give an overview of these algorithms and some of their applications.
	www.dfki.de /~nonnenga/publications/abstracts.html (1722 words)

	SCEAS
		An algorithm for constructing detaching bases in the ring of polynominals over a field.
		Algorithm 628: An Algorithm for Constructing Canonical Bases of Polynomial Ideals.
		A Geometrical Decision Algorithm Based on the Gröbner Bases Algorithm.
	delab.csd.auth.gr /sceas/php/search.php4?author_id=26504 (250 words)

	all.txt
		The Knuth-Bendix completion algorithm could in principle be used to systematically discover any other demodulators that would also have to be added.
		If the functor imageV were to be introduced, one would need the demodulator for imageV(V) in order to have a confluent set of demodulators.
	www.math.gatech.edu /~belinfan/research/autoreas/otter/sum/im/3/image_v/all.txt (344 words)

	Abstracts of Andreas Nonnengart's Bookchapters
		A short introduction into term rewriting systems.This chapter is supposed to provide beginners in logic with the basics of term rewriting, the Knuth-Bendix completion algorithm and theorem proving by rewriting.
	www.mpi-sb.mpg.de /~nonnenga/publications/bookchapters/abstracts.html (110 words)

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		Please contact the server administrator, serveradmin@explanation-guide.info and inform them of the time the error occurred, and anything you might have done that may have caused the error.
		More information about this error may be available in the server error log.
	explanation-guide.info /meaning/William-Bendix.html (55 words)

	A priori algorithm: Encyclopedia topic
		Other algorithms are designed for finding association rules in data having no transactions (Winepi and Minepi), or having no timestamps (dna sequencing).
		The algorithm generates candidate item sets (patterns) of length from length item sets.
		For determining frequent items in a fast manner, the algorithm uses a hash tree to store candidate itemsets.
	www.absoluteastronomy.com /reference/a_priori_algorithm (324 words)

	ORA Canada Bibliography of Automated Deduction: K-L
		[Kerchner 1983] H. Kerchner, A general completion algorithm for equational term rewriting systems and its proof of correctness.
		[Knuth 1970] D. Knuth, P. Bendix, Simple word problems in universal algebras, in Computational Problems in Abstract Algebras, ed.
		[Kirchner 1989c] C. Kirchner, From unification in combination of equational theories to a new AC-unification algorithm*, In: Resolution of Equations in Algebraic Structures: Vol 2, Rewriting Techniques, ed.
	www.ora.on.ca /biblio/biblio-prover-k-l.html (9619 words)

	Bibliography
		A Complete Proof of Correctness of the Knuth-Bendix Completion Algorithm.
		A Systematic Study of Infinite Canonical Systems generated by Knuth-Bendix Completion and Related Problems.
		A Critical-Pair Completion Algorithm for Finitely Generated Ideals in Rings.
	www.mathematik.uni-kl.de /~zca/Reports_on_ca/14/paper_html/node8.html (359 words)

	EUROCAM 1982
		Wolfgang Küchlin: A Theorem-Proving Approach to the Knuth-Bendix Completion Algorithm.
		Algorithms II Jacques Calmet, Rüdiger Loos: Deterministic Versus Probabilistic Factorization of Integral Polynomials.
		Arnold Schönhage: Asymptotically Fast Algorithms for the Numerical Multiplication and Division of Polynomials with Complex Coeficients.
	sunsite.informatik.rwth-aachen.de /dblp/db/conf/eurocal/eurocam1982.html (439 words)

	Definition of Timeline of algorithms
		1970 - Knuth-Bendix completion algorithm developed by Donald Knuth and P.
		1976 - Knuth-Morris-Pratt algorithm developed by Donald Knuth and Vaughan Pratt and independently by J.
		The following timeline outlines the development of algorithms since their inception.
	www.wordiq.com /definition/Timeline_of_algorithms (630 words)

	Claude Marché's PhD thesis (abstract)
		We obtain a new completion algorithm which contains as an instance the usual Knuth-Bendix completion algorithm, but also algorithms for computing standard bases of polynomial ideals, of Buchberger, and Kandri-Rody and Kapur.
		Finally, we have an implementation which shows the efficiency of normalized completion with respect to completion modulo AC.
		This rewrite relation allows us to rewrite modulo theories for which the previous notion was not applicable, including identity, idempotency, Abelian group theory and commutative ring theory.
	www.lri.fr /~marche/thesis.html (144 words)

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