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Formalizing KnuthBendix orders and KnuthBendix completion
 In Proc. RTA ’13, volume 21 of LIPIcs
, 2013
"... We present extensions of our Isabelle Formalization of Rewriting that cover two historically related concepts: the KnuthBendix order and the KnuthBendix completion procedure. The former, besides being the first development of its kind in a proof assistant, is based on a generalized version of the ..."
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Cited by 5 (2 self)
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We present extensions of our Isabelle Formalization of Rewriting that cover two historically related concepts: the KnuthBendix order and the KnuthBendix completion procedure. The former, besides being the first development of its kind in a proof assistant, is based on a generalized version
KnuthBendix Completion for NonSymmetric Transitive Relations
"... 1 Introduction Rewriting usually focuses on equational logic and term normal forms. In this context it yields solutions to word problems in certain free and finitely presented algebras via canonical term rewrite systems. The KnuthBendix procedure constructs such canonical systems incrementally from ..."
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from equational specifications. Equational rewriting and completion have been successfully integrated into automated firstorder and interactive higherorder deductive systems. Our main contribution is the specification, proof of correctness and discussion of KnuthBendix completion procedures beyond
Paramodulation and KnuthBendix Completion with Nontotal and Nonmonotonic Orderings
, 2001
"... Up to now, all existing completeness results for ordered paramodulation and KnuthBendix completion require the term ordering to be wellfounded, monotonic and total(izable) on ground terms. For several applications, these requirements are too strong, and hence weakening them has been a wellknown ..."
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Cited by 2 (1 self)
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Up to now, all existing completeness results for ordered paramodulation and KnuthBendix completion require the term ordering to be wellfounded, monotonic and total(izable) on ground terms. For several applications, these requirements are too strong, and hence weakening them has been a well
2011): Categorification, term rewriting and the KnuthBendix procedure
 J. of Pure and Appl. Alg
"... ABSTRACT. An axiomatization of a finitary, equational universal algebra by a convergent term rewrite system gives rise to a finite, coherent categorification of the algebra. ..."
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ABSTRACT. An axiomatization of a finitary, equational universal algebra by a convergent term rewrite system gives rise to a finite, coherent categorification of the algebra.
Declarative Graph Algorithms via KnuthBendix Completion
, 2002
"... We propose combined and cooperating KnuthBendix completion procedures for equalities and inequalities. They serve as metaprocedures for developing rulebased declarative algorithms. Here, we present algorithms for memoization, cycle detection and strongly connected components. The specifications ..."
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Cited by 1 (1 self)
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We propose combined and cooperating KnuthBendix completion procedures for equalities and inequalities. They serve as metaprocedures for developing rulebased declarative algorithms. Here, we present algorithms for memoization, cycle detection and strongly connected components
Inductive Inference for Solving Divergence in KnuthBendix Completion
 In Proceedings of Analogical and Inductive Inference 89, LNCS 397
, 1989
"... This paper presents an.approach to solving divergence in the KnuthBendix completion algorithm [Knuth/Bendix]. The KnuthBendix completion procedure generates a confluent set of rewrite rules by repeatedly superposing left hand sides of rewrite rules and adding any generated critical pairs as new ..."
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Cited by 4 (0 self)
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This paper presents an.approach to solving divergence in the KnuthBendix completion algorithm [Knuth/Bendix]. The KnuthBendix completion procedure generates a confluent set of rewrite rules by repeatedly superposing left hand sides of rewrite rules and adding any generated critical pairs as new
A userinterface for KnuthBendix completion
 In 4th Workshop on User Interfaces for Theorem Provers (UITP'98
, 1998
"... Introduction The KnuthBendix completion procedure, or more precisely the family of completion procedures, is at the heart of algebraic theorem proving and equational programming. In a theorem proving setting, it can be used for solving the word problem in a given algebra (is s equal to t modulo so ..."
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Cited by 3 (0 self)
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Introduction The KnuthBendix completion procedure, or more precisely the family of completion procedures, is at the heart of algebraic theorem proving and equational programming. In a theorem proving setting, it can be used for solving the word problem in a given algebra (is s equal to t modulo
KnuthBendix constraint solving is NPcomplete
 IN PROCEEDINGS OF 28TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP), VOLUME 2076 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2000
"... We show that the problem of solving KnuthBendix ordering constraints is NPcomplete, as a corollary we show that the existential firstorder theory of any term algebra with the KnuthBendix ordering is NPcomplete. ..."
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Cited by 11 (3 self)
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We show that the problem of solving KnuthBendix ordering constraints is NPcomplete, as a corollary we show that the existential firstorder theory of any term algebra with the KnuthBendix ordering is NPcomplete.
KnuthBendix Completion for NonSymmetric Transitive Relations
 Second International Workshop on RuleBased Programming (RULE2001), volume 59 of Electronic Notes in Theoretical Computer Science
, 2001
"... We extend the KnuthBendix completion procedure from equational rewriting to rewriting with nonsymmetric transitive relations and quasiorderings. The main dierences are the following: Specication of the general nonground case seems beyond rstorder logic. It is within rstorder logic when ter ..."
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Cited by 3 (3 self)
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We extend the KnuthBendix completion procedure from equational rewriting to rewriting with nonsymmetric transitive relations and quasiorderings. The main dierences are the following: Specication of the general nonground case seems beyond rstorder logic. It is within rstorder logic when
Termination of Ground NonSymmetric KnuthBendix Completion
, 2002
"... In the most natural approach, ground KnuthBendix completion procedures for nonsymmetric transitive relations and quasiorderings, as specified in [16], need not terminate. We use a twostep transformation on the input expressions to enforce termination after O(n) steps in the size of the input. ..."
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Cited by 1 (1 self)
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In the most natural approach, ground KnuthBendix completion procedures for nonsymmetric transitive relations and quasiorderings, as specified in [16], need not terminate. We use a twostep transformation on the input expressions to enforce termination after O(n) steps in the size of the input
Results 1  10
of
638,730