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About changing the ordering during Knuth-Bendix completion [chapter]

Andrea Sattler-Klein
1994 Lecture Notes in Computer Science  
a way that the reduction ordering used for completion can be changed during completion provided that the new ordering is compatible with the actual rules.  ...  Most existing implementations of the Knuth-Bendix algorithm provide the user with help in choosing a reduction ordering: If an unorientable equation is encountered, then the user has many options, especially  ...  The algorithm sketched here is due to Knuth and Bendix KB70] and known as the Knuth-Bendix completion algorithm (for SRSs).  ... 
doi:10.1007/3-540-57785-8_140 fatcat:unadxhzlbrakzdyro3x3rdt4fi

Slothrop: Knuth-Bendix Completion with a Modern Termination Checker [chapter]

Ian Wehrman, Aaron Stump, Edwin Westbrook
2006 Lecture Notes in Computer Science  
In this paper, we present a variant on the Knuth-Bendix completion procedure in which no ordering is assumed.  ...  While in principle any reduction ordering can be used, modern completion tools typically implement only Knuth-Bendix and path orderings.  ...  The authors are especially appreciative of Peter Schneider-Kamp and the AProVE team for their willingness to make changes to their system necessary for integration with Slothrop.  ... 
doi:10.1007/11805618_22 fatcat:vlnxqvmy5raefawmjqn5jo4vq4

Elimination of composite superpositions may cause abortion

Andrea Sattler-Klein
1991 Journal of symbolic computation  
We will show by examples that the elimination of composite superpositions during the completion of a term rewriting system may lead to an unnecessary stop with failure that cannot be prevented by postponing  ...  In that article the authors presented a criterion that can be used to eliminate critical pairs during the Knuth-Bendix completion of a term rewriting system.  ...  Thus, the Knuth-Bendix completion algorithm stops with failure.  ... 
doi:10.1016/s0747-7171(08)80045-4 fatcat:dqyluythn5ekzgcdsnuphcuqra

Strategy Compliant Multi-Threaded Term Completion

1996 Journal of symbolic computation  
We discuss the parallelization of three term completion procedures: Knuth-Bendix completion, completion modulo AC, and unfailing completion.  ...  PaReDuX now contains data-structures and algorithms for parallel Knuth-Bendix completion of plain term-rewriting systems (Knuth and Bendix, 1970) , of completion modulo associativity and commutativity  ...  We thank Patrick Maier for his contribution to implementing the parallel unfailing completion procedure.  ... 
doi:10.1006/jsco.1996.0027 fatcat:pkdvonnn2naxfhrcav7bxrel3e

Page 1603 of Mathematical Reviews Vol. , Issue 92c [page]

1992 Mathematical Reviews  
We also point out how to perform the construction incrementally, which makes our approach suitable for applications in which pattern sets change dynamically, as in the Knuth-Bendix completion algorithm  ...  Using this method, a variation of the Knuth-Bendix completion procedure can be used for automat- ically proving equations by induction.  ... 

Knuth-Bendix for groups with infinitely many rules [article]

D. B. A. Epstein, P. J. Sanders
2000 arXiv   pre-print
It is shown how to use a small finite state automaton in two variables in order to carry out the Knuth-Bendix process for rewriting words in a group in shortlex order.  ...  The two-variable automaton can be used to store an infinite set of rules and to carry out fast reduction of arbitrary words using this infinite set.  ...  S will continually change, while Rules is constant during a Knuth-Bendix pass. We change Rules at the end of each Knuth-Bendix pass.  ... 
arXiv:math/0001035v1 fatcat:ru6566y22bgyzb3q3urj357hoi

A fine-grained parallel completion procedure

Reinhard Bündgen, Manfred Göbel, Wolfgang Küchlin
1994 Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '94  
We present a parallel Knuth-Bendiz completion algorithm where the inner loop, deriving the consequences of adding a new rule to the system, is multi-threaded.  ...  The selection of the best new rule in the outer loop, and hence the completion strategy, is exactly the same as for the sequential algorithm.  ...  We also thank Michael Sperber for his implementation of the ALDES-to-C Compiler and Nick Nevin and Jeff Ward for their contributions to the S-threads system.  ... 
doi:10.1145/190347.190427 dblp:conf/issac/BundgenGK94 fatcat:m2dwt3dhtvg6haikc4bqjbtrre

A Homotopical Completion Procedure with Applications to Coherence of Monoids

Yves Guiraud, Philippe Malbos, Samuel Mimram, Marc Herbstritt
2013 International Conference on Rewriting Techniques and Applications  
We extend the Knuth-Bendix completion procedure to this setting, resulting in a homotopical completion procedure.  ...  The Knuth-Bendix completion. This recipe for constructing presentations does not always work as easily.  ...  type A 2 ).Perform a Knuth-Bendix completion.Add the Kapur-Narendran generator.Perform a Knuth-Bendix completion.  ... 
doi:10.4230/lipics.rta.2013.223 dblp:conf/rta/GuiraudMM13 fatcat:4yvenczcn5dlfdjfao552y4ynm

Proving a group trivial made easy: A case study in coset enumeration

George Havas, Colin Ramsay
2000 Bulletin of the Australian Mathematical Society  
Neumann, on the occasion of his 90th birthday Coset enumeration, based on the methods described by Todd and Coxeter, is one of the basic tools for investigating finitely presented groups.  ...  We show that the problems are much easier than they first appear, albeit at the expense of considerable preliminary 'experimentation'.  ...  For the memory requirements of the Knuth-Bendix programmes we quote the maximum total length of the rules (both sides) during a calculation.  ... 
doi:10.1017/s0004972700018529 fatcat:dmyg2x6cajci7eb7xz7aon42em

History and basic features of the critical-pair/completion procedure

Bruno Buchberger
1987 Journal of symbolic computation  
A synopsis of the critical-pair/completion approach for solving algorithmic problems in theorem proving, finitely generated algebras and rewrite systems is given.  ...  The presentation is biased towards the development of the approach in algorithmic polynomial ideal theory.  ...  Lankford proposed using the Knuth-Bendix procedure in connection with the resolution method in order to complete the sets of equalities used in the resolution method.  ... 
doi:10.1016/s0747-7171(87)80020-2 fatcat:qseoki5m6ff2bikdyubumx3b24

Knuth-Bendix constraint solving is NP-complete [article]

Konstantin Korovin, Andrei Voronkov
2002 arXiv   pre-print
We show the NP-completeness of the existential theory of term algebras with the Knuth-Bendix order by giving a nondeterministic polynomial-time algorithm for solving Knuth-Bendix ordering constraints.  ...  As a consequence, we obtain that the existential first-order theory of any term algebra with a Knuth-Bendix order is NP-complete too.  ...  Theorem 5.2: The existential first-order theory of any term algebra with the Knuth-Bendix order in a signature with at least two symbols is NP-complete.  ... 
arXiv:cs/0207068v1 fatcat:3nkk43lfzjfnxi4oewbwai2foi

Detecting looping simplifications [chapter]

Paul Walton Purdom
1987 Lecture Notes in Computer Science  
Experiments suggest that the simplest form of the algorithm is about 80 percent effective in eliminating bad orientations of rules.  ...  Given the equation s = t, this algorithm can often quickly determine that the rewrite rule s --+ t leads to an infinite sequence of "simplifications". The rule t --~ 8 can be tested in the same way.  ...  The loop test could eliminate about half of the possible orderings, potentially saving about half the time used by the termination ordering algorithm. m U-match(s, t, c).  ... 
doi:10.1007/3-540-17220-3_5 fatcat:ez7wzrjbj5d6fnuxfdff4v2xbe

Automatic Groups and Knuth-Bendix with Infinitely Many Rules [article]

D. B. A. Epstein, Paul J. Sanders
1998 arXiv   pre-print
It is shown how to use a small finite state automaton in two variables in order to carry out part of the Knuth--Bendix process for rewriting words in a group.  ...  The main objective is to provide a substitute for the most space-demanding module of the existing software which attempts to find a shortlex-automatic structure for a group.  ...  In this case it might be advisable to abort the current Knuth-Bendix pass. To see if abortion is advisable, we can record statistics about how much WDiff has changed since the beginning of a pass.  ... 
arXiv:math/9805057v1 fatcat:22kv4f33nnawbjvxfi5hmkvg5e

On solving the equality problem in theories defined by Horn clauses

E. Paul
1986 Theoretical Computer Science  
In this paper we propose a slight modification of the Knuth and Bendix completion procedure for solving the equality problem in nonequational theories defined by a set of Horn clauses.  ...  In particular, we need only the reflexivity axiom for equality. Another application of the Knuth and Bendix procedure is the proof by induction (Musser, 1980; Huet-Hullot, 1982 and others).  ...  We assume familiarity with the Knuth-Bendix completion algorithm, as presented in [12] .  ... 
doi:10.1016/0304-3975(86)90114-3 fatcat:5klyzsqzf5h4vi4pamasubukjy

Page 4902 of Mathematical Reviews Vol. , Issue 95h [page]

1995 Mathematical Reviews  
{For the entire collection see MR 95e:68005. } 95h:68103 68Q42 Sattler-Klein, Andrea (D-KSRL-I; Kaiserslautern) About changing the ordering during Knuth-Bendix completion.  ...  used for completion can be changed during completion to a new ordering that is compatible with the ac- tual rules.  ... 
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