Results 1  10
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1,189
A nullstellensatz with nilpotents and Zariski’s main lemma on holomorphic functions
 J. Algebra
, 1979
"... The classical Nullstellensatz asserts that a reduced affine variety is known by its closed points; algebraically, a prime ideal in an affine ring is the intersection of the maximal ideals containing it. A leading special case of our theorem says that any affine scheme can be distinguished from its s ..."
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Cited by 15 (3 self)
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of as a sharpening of Zariski’s Main Lemma on holomorphic functions [4]. Roughly speaking, this lemma asserts that if a regular function f on an irreducible affine variety V vanishes to order e at each of a dense set JV of closed points of V, then it vanishes to order e at the generic point; that is, if P
The Semantics Of Constraint Logic Programs
 JOURNAL OF LOGIC PROGRAMMING
, 1996
"... This paper presents for the first time the semantic foundations of CLP in a selfcontained and complete package. The main contributions are threefold. First, we extend the original conference paper by presenting definitions and basic semantic constructs from first principles, giving new and comp ..."
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Cited by 872 (14 self)
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and complete proofs for the main lemmas. Importantly, we clarify which theorems depend on conditions such as solution compactness, satisfaction completeness and independence of constraints. Second, we generalize the original results to allow for incompleteness of the constraint solver. This is important
A Simple Proof of the Restricted Isometry Property for Random Matrices
 CONSTR APPROX
, 2008
"... We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices that underlies Compressed Sensing. Our approach has two main ingredients: (i) concentration inequalities for random inner products that have recently provided algorithmical ..."
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Cited by 631 (64 self)
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We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices that underlies Compressed Sensing. Our approach has two main ingredients: (i) concentration inequalities for random inner products that have recently provided
Almost Optimal Lower Bounds for Small Depth Circuits
, 1986
"... We give improved lower bounds for the size of small depth circuits computing several functions. In particular we prove almost optimal lower bounds for the size of parity circuits. Further we show that there are functions computable in polynomial size and depth k but requires exponential size when ..."
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Cited by 277 (8 self)
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when the depth is restricted to k1. Our main lemma which is of independent interest states that by using a random restriction we can convert an AND of small ORs to an OR of small ANDs and conversely.
Stable Distributions, Pseudorandom Generators, Embeddings and Data Stream Computation
, 2000
"... In this paper we show several results obtained by combining the use of stable distributions with pseudorandom generators for bounded space. In particular: ffl we show how to maintain (using only O(log n=ffl 2 ) words of storage) a sketch C(p) of a point p 2 l n 1 under dynamic updates of its coo ..."
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Cited by 324 (13 self)
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coordinates, such that given sketches C(p) and C(q) one can estimate jp \Gamma qj 1 up to a factor of (1 + ffl) with large probability. This solves the main open problem of [10]. ffl we obtain another sketch function C 0 which maps l n 1 into a normed space l m 1 (as opposed to C), such that m = m
Algorithms and Complexity Concerning the Preemptive Scheduling of Periodic, RealTime Tasks on One Processor
 RealTime Systems
, 1990
"... We investigate the preemptive scheduling of periodic, realtime task systems on one processor. First, we show that when all parameters to the system are integers, we may assume without loss of generality that all preemptions occur at integer time values. We then assume, for the remainder of the pape ..."
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Cited by 248 (15 self)
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of the paper, that all parameters are indeed integers. We then give as our main lemma both necessary and sufficient conditions for a task system to be feasible on one processor. Although these conditions cannot, in general, be tested efficiently (unless P = NP), they do allow us to give efficient algorithms
Pseudorandom generators without the XOR Lemma (Extended Abstract)
, 1998
"... Impagliazzo and Wigderson [IW97] have recently shown that if there exists a decision problem solvable in time 2 O(n) and having circuit complexity 2 n) (for all but finitely many n) then P = BPP. This result is a culmination of a series of works showing connections between the existence of har ..."
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Cited by 138 (23 self)
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of hard predicates and the existence of good pseudorandom generators. The construction of Impagliazzo and Wigderson goes through three phases of "hardness amplification" (a multivariate polynomial encoding, a first derandomized XOR Lemma, and a second derandomized XOR Lemma) that are composed
Isoperimetric Problems for Convex Bodies and a Localization Lemma
, 1995
"... We study the smallest number /(K) such that a given convex body K in IR n can be cut into two parts K 1 and K 2 by a surface with an (n \Gamma 1)dimensional measure /(K)vol(K 1 ) \Delta vol(K 2 )=vol(K). Let M 1 (K) be the average distance of a point of K from its center of gravity. We prove for ..."
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Cited by 133 (9 self)
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for the "isoperimetric coefficient" that /(K) ln 2 M 1 (K) ; and give other upper and lower bounds. We conjecture that our upper bound is best possible up to a constant. Our main tool is a general "Localization Lemma" that reduces integral inequalities over the ndimensional space
A survey of the Slemma
 SIAM Review
"... Abstract. In this survey we review the many faces of the Slemma, a result about the correctness of the Sprocedure. The basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization, convex geometry, and linear algebra as ..."
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Cited by 63 (1 self)
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as well. These were all active research areas, but as there was little interaction between researchers in these different areas, their results remained mainly isolated. Here we give a unified analysis of the theory by providing three different proofs for the Slemma and revealing hidden connections
Results 1  10
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1,189