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Orienting Equalities with the KnuthBendix Order
"... Orientability of systems of equalities is the following problem: given a system of equalities s 1 t 1 , . . . , s n t n , does there exist a simplification ordering which orients the system, that is for every i ..., n}, either s i t i or t i s i . This problem can be used in rewriting for finding a ..."
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canonical rewrite system for a system of equalities and in theorem proving for adjusting simplification orderings during completion. We prove that (rather surprisingly) the problem can be solved in polynomial time when we restrict ourselves to the KnuthBendix orderings.
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
An ACCompatible KnuthBendix Order
"... We introduce a family of ACcompatible KnuthBendix simplification orders which are ACtotal on ground terms. Our orders preserve attractive features of the original KnuthBendix orders such as existence of a polynomialtime algorithm for comparing terms; computationally e#cient approximations, for ..."
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Cited by 4 (1 self)
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We introduce a family of ACcompatible KnuthBendix simplification orders which are ACtotal on ground terms. Our orders preserve attractive features of the original KnuthBendix orders such as existence of a polynomialtime algorithm for comparing terms; computationally e#cient approximations
Orienting rewrite rules with the KnuthBendix order
 Information and Computation
"... 2). We show that both the orientability problem is Pcomplete. Also we show that if a system is orientable using a realvalued instance of KBO, then it is also orientable using an integervalued instance of KBO. Therefore, all our results hold both for the integervalued and the realvalued KBO. 1 I ..."
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Cited by 13 (1 self)
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2). We show that both the orientability problem is Pcomplete. Also we show that if a system is orientable using a realvalued instance of KBO, then it is also orientable using an integervalued instance of KBO. Therefore, all our results hold both for the integervalued and the realvalued KBO. 1
Extensions of the KnuthBendix ordering with LPOlike properties
, 2007
"... The KnuthBendix ordering is usually preferred over the lexicographic path ordering in successful implementations of resolution and superposition calculi. However, it is incompatible with certain requirements of hierarchic superposition calculi, and it also does not allow nonlinear definition equat ..."
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Cited by 11 (0 self)
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equations to be oriented in a natural way. We present two extensions of the KnuthBendix ordering that make it possible to overcome these restrictions. 1
The Decidability of the Firstorder Theory of KnuthBendix Order
"... Abstract. Two kinds of orderings are widely used in term rewriting and theorem proving, namely recursive path ordering (RPO) and KnuthBendix ordering (KBO). They provide powerful tools to prove the termination of rewriting systems. They are also applied in ordered resolution to prune the search spa ..."
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Cited by 5 (0 self)
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Abstract. Two kinds of orderings are widely used in term rewriting and theorem proving, namely recursive path ordering (RPO) and KnuthBendix ordering (KBO). They provide powerful tools to prove the termination of rewriting systems. They are also applied in ordered resolution to prune the search
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
Unifying the KnuthBendix, recursive path and polynomial orders
 In Proc. PPDP ’13
, 2013
"... We introduce a simplification order called the weighted path order (WPO). WPO compares weights of terms as in the KnuthBendix order (KBO), while WPO allows weights to be computed by an arbitrary interpretation which is weakly monotone and weakly simple. We investigate summations, polynomials and ma ..."
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Cited by 4 (2 self)
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We introduce a simplification order called the weighted path order (WPO). WPO compares weights of terms as in the KnuthBendix order (KBO), while WPO allows weights to be computed by an arbitrary interpretation which is weakly monotone and weakly simple. We investigate summations, polynomials
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.
Results 1  10
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958,765