Results 1  10
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1,268
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 961 (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
Tensor network nonzero testing
, 2014
"... Tensor networks are a central tool in condensed matter physics. In this paper, we initiate the study of tensor network nonzero testing (TNZ): Given a tensor network T, does T represent a nonzero vector? We show that TNZ is not in the PolynomialTime Hierarchy unless the hierarchy collapses. We nex ..."
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Tensor networks are a central tool in condensed matter physics. In this paper, we initiate the study of tensor network nonzero testing (TNZ): Given a tensor network T, does T represent a nonzero vector? We show that TNZ is not in the PolynomialTime Hierarchy unless the hierarchy collapses. We
Two remarks on nonzero constant Jacobian polynomial map of C²
, 2004
"... We present some estimations on geometry of the exceptional value sets of nonzero constant Jacobian polynomial maps of C² and it’s components. ..."
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Cited by 1 (1 self)
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We present some estimations on geometry of the exceptional value sets of nonzero constant Jacobian polynomial maps of C² and it’s components.
How to Go Beyond the BlackBox Simulation Barrier
 In 42nd FOCS
, 2001
"... The simulation paradigm is central to cryptography. A simulator is an algorithm that tries to simulate the interaction of the adversary with an honest party, without knowing the private input of this honest party. Almost all known simulators use the adversary’s algorithm as a blackbox. We present t ..."
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Cited by 228 (13 self)
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polynomial time. All previously known constantround, negligibleerror zeroknowledge arguments utilized expected polynomialtime simulators.
Cartesian Genetic Programming
, 2000
"... This paper presents a new form of Genetic Programming called Cartesian Genetic Programming in which a program is represented as an indexed graph. The graph is encoded in the form of a linear string of integers. The inputs or terminal set and node outputs are numbered sequentially. The node funct ..."
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Cited by 230 (59 self)
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) is examined and compared with nonneutral search for the Santa Fe ant problem. The neutral search...
Evaluating 2dnf formulas on ciphertexts
 In proceedings of TCC ’05, LNCS series
, 2005
"... Abstract. Let ψ be a 2DNF formula on boolean variables x1,..., xn ∈ {0, 1}. We present a homomorphic public key encryption scheme that allows the public evaluation of ψ given an encryption of the variables x1,..., xn. In other words, given the encryption of the bits x1,..., xn, anyone can create th ..."
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Cited by 231 (7 self)
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Ostrovsky PIR protocol is reduced from √ n to 3 √ n. 2. An efficient election system based on homomorphic encryption where voters do not need to include noninteractive zero knowledge proofs that their ballots are valid. The election system is proved secure without random oracles but still efficient. 3. A
Estimating certain nonzero LittlewoodRichardson coefficients
 in Proc. FPSAC 2014 ; arXiv:1306.4060
"... Littlewood Richardson coefficients are structure constants appearing in the representation theory of the general linear groups (GLn). The main results of this paper are: 1. A strongly polynomial randomized approximation scheme for certain LittlewoodRichardson coefficients. 2. A proof of approxima ..."
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Cited by 2 (1 self)
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Littlewood Richardson coefficients are structure constants appearing in the representation theory of the general linear groups (GLn). The main results of this paper are: 1. A strongly polynomial randomized approximation scheme for certain LittlewoodRichardson coefficients. 2. A proof
Learning Decision Trees using the Fourier Spectrum
, 1991
"... This work gives a polynomial time algorithm for learning decision trees with respect to the uniform distribution. (This algorithm uses membership queries.) The decision tree model that is considered is an extension of the traditional boolean decision tree model that allows linear operations in each ..."
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Cited by 207 (10 self)
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node (i.e., summation of a subset of the input variables over GF (2)). This paper shows how to learn in polynomial time any function that can be approximated (in norm L 2 ) by a polynomially sparse function (i.e., a function with only polynomially many nonzero Fourier coefficients). The authors
On the complexity of the parity argument and other inefficient proofs of existence
 JCSS
, 1994
"... We define several new complexity classes of search problems, "between " the classes FP and FNP. These new classes are contained, along with factoring, and the class PLS, in the class TFNP of search problems in FNP that always have a witness. A problem in each of these new classes is define ..."
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Cited by 205 (8 self)
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, Chfvalley's theorem, and the BorsukUlam theorem, the linear complementarity problem for Pmatrices, finding a mixed equilibrium in a nonzero sum game, finding a second Hamilton circuit in a Hamiltonian cubic graph, a second Hamiltonian decomposition in a quartic graph, and others. Some
Digital step edges from zero crossing of second directional derivatives
 Pattern Analysis and Machine Intelligence, IEEE Transactions on
, 1984
"... AbstractWe use the facet model to accomplish step edge detection. The essence of the facet model is that any analysis made on the basis of the pixel values in some neighborhood has its final authoritative interpretation relative to the underlying gray tone intensity surface of which the neighborho ..."
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Cited by 200 (5 self)
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the neighborhood pixel values are observed noisy samples. With regard to edge detection, we define an edge to occur in a pixel if and only if there is some point in the pixel's area having a negatively sloped zero crossing of the second directional derivative taken in the direction of a nonzero gradient
Results 1  10
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