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563,688
Factoring polynomials with rational coefficients
 MATH. ANN
, 1982
"... In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive polynomia ..."
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Cited by 982 (11 self)
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In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive
The Askeyscheme of hypergeometric orthogonal polynomials and its qanalogue
, 1998
"... We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a q analogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order di#erent ..."
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Cited by 580 (6 self)
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We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a q analogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order di
The knowledge complexity of interactive proof systems
 in Proc. 27th Annual Symposium on Foundations of Computer Science
, 1985
"... Abstract. Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/nonHamiltoni ..."
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Cited by 1267 (42 self)
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Abstract. Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non
Simulating Physics with Computers
 SIAM Journal on Computing
, 1982
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 601 (1 self)
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A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration
Algorithms for Quantum Computation: Discrete Logarithms and Factoring
, 1994
"... A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a increase in computation time of at most a polynomial factor. It is not clear whether this is still true when quantum mechanics is taken into consi ..."
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Cited by 1103 (7 self)
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A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a increase in computation time of at most a polynomial factor. It is not clear whether this is still true when quantum mechanics is taken
NonMalleable Cryptography
 SIAM Journal on Computing
, 2000
"... The notion of nonmalleable cryptography, an extension of semantically secure cryptography, is defined. Informally, in the context of encryption the additional requirement is that given the ciphertext it is impossible to generate a different ciphertext so that the respective plaintexts are related. ..."
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Cited by 490 (21 self)
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. The same concept makes sense in the contexts of string commitment and zeroknowledge proofs of possession of knowledge. Nonmalleable schemes for each of these three problems are presented. The schemes do not assume a trusted center; a user need not know anything about the number or identity of other
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We also argue that most known interior point methods for linear programs can be transformed in a
Training Support Vector Machines: an Application to Face Detection
, 1997
"... We investigate the application of Support Vector Machines (SVMs) in computer vision. SVM is a learning technique developed by V. Vapnik and his team (AT&T Bell Labs.) that can be seen as a new method for training polynomial, neural network, or Radial Basis Functions classifiers. The decision sur ..."
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Cited by 728 (1 self)
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We investigate the application of Support Vector Machines (SVMs) in computer vision. SVM is a learning technique developed by V. Vapnik and his team (AT&T Bell Labs.) that can be seen as a new method for training polynomial, neural network, or Radial Basis Functions classifiers. The decision
Boosting a Weak Learning Algorithm By Majority
, 1995
"... We present an algorithm for improving the accuracy of algorithms for learning binary concepts. The improvement is achieved by combining a large number of hypotheses, each of which is generated by training the given learning algorithm on a different set of examples. Our algorithm is based on ideas pr ..."
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Cited by 516 (15 self)
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presented by Schapire in his paper "The strength of weak learnability", and represents an improvement over his results. The analysis of our algorithm provides general upper bounds on the resources required for learning in Valiant's polynomial PAC learning framework, which are the best general
Large margin methods for structured and interdependent output variables
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... Learning general functional dependencies between arbitrary input and output spaces is one of the key challenges in computational intelligence. While recent progress in machine learning has mainly focused on designing flexible and powerful input representations, this paper addresses the complementary ..."
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Cited by 612 (12 self)
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that solves the optimization problem in polynomial time for a large class of problems. The proposed method has important applications in areas such as computational biology, natural language processing, information retrieval/extraction, and optical character recognition. Experiments from various domains
Results 1  10
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563,688