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The knowledge complexity of interactive proof systems

, 1989
"... 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/nonHamiltonian. In th ..."
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Cited by 1246 (39 self)
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/nonHamiltonian. In this paper a computational complexity theory of the "knowledge " contained in a proof is developed. Zeroknowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zeroknowledge proof systems are given
Symmetric and Quadratic Complexes with Geometric Control
 Proceedings of TGRCKOSEF
, 1993
"... this paper we only deal with the cases A = Z and A = Z[Z 2 ], so assume that A is commutative ..."
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Cited by 4 (3 self)
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this paper we only deal with the cases A = Z and A = Z[Z 2 ], so assume that A is commutative
On the absolute quadratic complex and its application to autocalibration
, 2005
"... Abstract. This article introduces the absolute quadratic complex formed by all lines that intersect the absolute conic. If ω denotes the 3 × 3 symmetric matrix representing the image of that conic under the action of a camera with projection matrix P, it is shown that ω ≈ PΩP T, where P is the 3×6 l ..."
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Cited by 10 (1 self)
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Abstract. This article introduces the absolute quadratic complex formed by all lines that intersect the absolute conic. If ω denotes the 3 × 3 symmetric matrix representing the image of that conic under the action of a camera with projection matrix P, it is shown that ω ≈ PΩP T, where P is the 3
Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
, 1998
"... SeDuMi is an addon for MATLAB, that lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity. This pape ..."
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Cited by 1368 (5 self)
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SeDuMi is an addon for MATLAB, that lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity
Interiorpoint Methods
, 2000
"... The modern era of interiorpoint methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadrati ..."
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Cited by 612 (15 self)
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quadratic programming, semidefinite programming, and nonconvex and nonlinear problems, have reached varying levels of maturity. We review some of the key developments in the area, including comments on both the complexity theory and practical algorithms for linear programming, semidefinite programming
Efficient belief propagation for early vision
 In CVPR
, 2004
"... Markov random field models provide a robust and unified framework for early vision problems such as stereo, optical flow and image restoration. Inference algorithms based on graph cuts and belief propagation yield accurate results, but despite recent advances are often still too slow for practical u ..."
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Cited by 515 (8 self)
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use. In this paper we present new algorithmic techniques that substantially improve the running time of the belief propagation approach. One of our techniques reduces the complexity of the inference algorithm to be linear rather than quadratic in the number of possible labels for each pixel, which
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 624 (12 self)
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the complementary issue of designing classification algorithms that can deal with more complex outputs, such as trees, sequences, or sets. More generally, we consider problems involving multiple dependent output variables, structured output spaces, and classification problems with class attributes. In order
Moduli spaces of quadratic complexes and their singular surfaces
, 2007
"... We construct the coarse moduli space Mqc(σ) of quadratic line complexes with a fixed Segre symbol σ as well as the moduli space Mss(σ) of the corresponding singular surfaces. We show that the map associating to a quadratic line complex its singular surface induces a morphism π: Mqc(σ) → Mss(σ). Fin ..."
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Cited by 4 (0 self)
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We construct the coarse moduli space Mqc(σ) of quadratic line complexes with a fixed Segre symbol σ as well as the moduli space Mss(σ) of the corresponding singular surfaces. We show that the map associating to a quadratic line complex its singular surface induces a morphism π: Mqc(σ) → Mss
The Union of Unit Balls Has Quadratic Complexity, Even If They All Contain the Origin
, 1999
"... We provide a lower bound construction showing that the union of unit balls in R³ has quadratic complexity, even if they all contain the origin. This settles a conjecture of Sharir. ..."
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Cited by 2 (0 self)
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We provide a lower bound construction showing that the union of unit balls in R³ has quadratic complexity, even if they all contain the origin. This settles a conjecture of Sharir.
Results 1  10
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