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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.
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.
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
KnuthBendix Completion with a Termination Checker
"... Abstract. KnuthBendix completion takes as input a set of universal equations and attempts to generate a convergent rewriting system with the same equational theory. An essential parameter is a reduction order used at runtime to ensure termination of intermediate rewriting systems. Any reduction ord ..."
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Abstract. KnuthBendix completion takes as input a set of universal equations and attempts to generate a convergent rewriting system with the same equational theory. An essential parameter is a reduction order used at runtime to ensure termination of intermediate rewriting systems. Any reduction
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
A decision procedure for the existential theory of term algebras with the KnuthBendix ordering
, 2000
"... We show the decidability of the existential theory of term algebras with any KnuthBendix ordering by giving a procedure for solving KnuthBendix ordering constraints. ..."
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Cited by 12 (4 self)
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We show the decidability of the existential theory of term algebras with any KnuthBendix ordering by giving a procedure for solving KnuthBendix ordering constraints.
Constraint Networks
, 1992
"... Constraintbased reasoning is a paradigm for formulating knowledge as a set of constraints without specifying the method by which these constraints are to be satisfied. A variety of techniques have been developed for finding partial or complete solutions for different kinds of constraint expression ..."
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Cited by 1149 (43 self)
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Constraintbased reasoning is a paradigm for formulating knowledge as a set of constraints without specifying the method by which these constraints are to be satisfied. A variety of techniques have been developed for finding partial or complete solutions for different kinds of constraint
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
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
Results 1  10
of
139,355