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683,040
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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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
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 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.
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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class of orders. Finding and specifying a compatible order, even among a small number of classes, is challenging in practice and crucial to the success of the method. In this work, a new variant on the KnuthBendix completion procedure is developed in which no order is provided by the user. Modern
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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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
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
AUTOMATIC GROUPS AND KNUTH–BENDIX WITH INFINITELY MANY RULES
, 1998
"... Abstract. 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 spacedemanding module of the existing software which attempts to find a ..."
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Abstract. 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 spacedemanding module of the existing software which attempts to find a
Knuth–Bendix for groups with infinitely many rules ∗
, 2008
"... We introduce a new class of groups with solvable word problem, namely groups specified by a confluent set of shortlexreducing Knuth– Bendix rules which form a regular language. This simultaneously generalizes shortlexautomatic groups and groups with a finite confluent set of shortlexreducing r ..."
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We introduce a new class of groups with solvable word problem, namely groups specified by a confluent set of shortlexreducing Knuth– Bendix rules which form a regular language. This simultaneously generalizes shortlexautomatic groups and groups with a finite confluent set of short
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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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
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683,040