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An Efficient Unification Algorithm
 TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS (TOPLAS)
, 1982
"... The unification problem in firstorder predicate calculus is described in general terms as the solution of a system of equations, and a nondeterministic algorithm is given. A new unification algorithm, characterized by having the acyclicity test efficiently embedded into it, is derived from the nond ..."
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Cited by 370 (1 self)
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The unification problem in firstorder predicate calculus is described in general terms as the solution of a system of equations, and a nondeterministic algorithm is given. A new unification algorithm, characterized by having the acyclicity test efficiently embedded into it, is derived from
An Algorithm for Solving Systems of Linear Diophantine . . .
 IN NATURALS. PROC. EPIA'97, LNAI 1323
, 1997
"... A new algorithm for finding the minimal solutions of systems of linear Diophantine equations has recently been published. In its description the emphasis was put on the mathematical aspects of the algorithm. In complement to that, in this paper another presentation of the algorithm is given which m ..."
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Cited by 2 (1 self)
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A new algorithm for finding the minimal solutions of systems of linear Diophantine equations has recently been published. In its description the emphasis was put on the mathematical aspects of the algorithm. In complement to that, in this paper another presentation of the algorithm is given which
Solving Linear Diophantine Equations
 REPORTS OF THE INSTITUTE OF CYBERNETICS
"... An overview of a family of methods for finding the minimal solutions to a single linear Diophantine equation over the natural numbers is given. Most of the formal details were dropped, some illustrations that might give some intuition on the methods being presented instead. ..."
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Cited by 2 (0 self)
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An overview of a family of methods for finding the minimal solutions to a single linear Diophantine equation over the natural numbers is given. Most of the formal details were dropped, some illustrations that might give some intuition on the methods being presented instead.
Solving Linear Diophantine Constraints Incrementally
 PROC. OF 10TH INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING
, 1993
"... In this paper, we show how to handle linear Diophantine constraints incrementally by using several variations of the algorithm by Contejean and Devie (hereafter called ABCD) for solving linear Diophantine systems [4, 5]. The basic algorithm is based on a certain enumeration of the potential solution ..."
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Cited by 11 (0 self)
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solutions of a system, and termination is ensured by an adequate restriction on the search. This algorithm generalizes a previous algorithm due to Fortenbacher [2], which was restricted to the case of a single equation. Note that using Fortenbacher's algorithm for solving systems of Diophantine
A review of algebraic multigrid
, 2001
"... Since the early 1990s, there has been a strongly increasing demand for more efficient methods to solve large sparse, unstructured linear systems of equations. For practically relevant problem sizes, classical onelevel methods had already reached their limits and new hierarchical algorithms had to b ..."
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Cited by 344 (11 self)
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Since the early 1990s, there has been a strongly increasing demand for more efficient methods to solve large sparse, unstructured linear systems of equations. For practically relevant problem sizes, classical onelevel methods had already reached their limits and new hierarchical algorithms had
DIOPHANTINE EQUATIONS AND DIOPHANTINE APPROXIMATION
"... Originally, Diophantine approximation is the branch of number theory dealing with problems such as whether a given real number is rational or irrational, or whether it is algebraic or transcendental. More generally, for a given irrational number one may ask how well it is approximable by a rational ..."
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Originally, Diophantine approximation is the branch of number theory dealing with problems such as whether a given real number is rational or irrational, or whether it is algebraic or transcendental. More generally, for a given irrational number one may ask how well it is approximable by a rational
Fast methods for solving linear diophantine equations
 Proceedings of the 6th Portuguese Conference on Artificial Intelligence, 727
, 1993
"... Abstract. We present some recent results from our research on methods for finding the minimal solutions to linear Diophantine equations over the naturals. We give an overview of a family of methods we developed and describe two of them, called Slopes algorithm and Rectangles algorithm. From empirica ..."
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Cited by 7 (4 self)
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Abstract. We present some recent results from our research on methods for finding the minimal solutions to linear Diophantine equations over the naturals. We give an overview of a family of methods we developed and describe two of them, called Slopes algorithm and Rectangles algorithm. From
Unification algebras: an axiomatic approach to unification, equation solving and constraint solving
 UNIVERSITAT KAISERSLAUTERN
, 1988
"... Traditionally unification is viewed as solving an equation in an algebra given an explicit construction method for terms and substitutions. We abstract from this explicit term construction methods and give a set of axioms describing unification algebras that consist of objects and mappings, where ob ..."
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Cited by 3 (0 self)
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Traditionally unification is viewed as solving an equation in an algebra given an explicit construction method for terms and substitutions. We abstract from this explicit term construction methods and give a set of axioms describing unification algebras that consist of objects and mappings, where
Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations
 IN ADVANCES IN CRYPTOLOGY, EUROCRYPT’2000, LNCS 1807
, 2000
"... The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NPhard over any field. When the number of equations m is the same as the number of unknowns n the best known algorithms are exhaus ..."
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Cited by 182 (20 self)
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are exhaustive search for small fields, and a Gröbner base algorithm for large fields. Gröbner base algorithms have large exponential complexity and cannot solve in practice systems with n ≥ 15. Kipnis and Shamir [9] have recently introduced a new algorithm called ”relinearization”. The exact complexity
Results 1  10
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634,552