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Completeness and Weak Completeness under PolynomialSize Circuits
 Information and Computation
, 1996
"... This paper investigates the distribution and nonuniform complexity of problems that are complete or weakly complete for ESPACE under nonuniform reductions that are computed by polynomialsize circuits (P/PolyTuring reductions and P/Polymanyone reductions). A tight, exponential lower bound on the ..."
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Cited by 8 (4 self)
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This paper investigates the distribution and nonuniform complexity of problems that are complete or weakly complete for ESPACE under nonuniform reductions that are computed by polynomialsize circuits (P/PolyTuring reductions and P/Polymanyone reductions). A tight, exponential lower bound
The strength of weak learnability
 Machine Learning
, 1990
"... Abstract. This paper addresses the problem of improving the accuracy of an hypothesis output by a learning algorithm in the distributionfree (PAC) learning model. A concept class is learnable (or strongly learnable) if, given access to a Source of examples of the unknown concept, the learner with h ..."
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Cited by 861 (24 self)
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with high probability is able to output an hypothesis that is correct on all but an arbitrarily small fraction of the instances. The concept class is weakly learnable if the learner can produce an hypothesis that performs only slightly better than random guessing. In this paper, it is shown that these two
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
AND and/or OR: Uniform PolynomialSize Circuits
"... We investigate the complexity of uniform OR circuits and AND circuits of polynomialsize and depth. As their name suggests, OR circuits have OR gates as their computation gates, as well as the usual input, output and constant 0/1 gates. As is the norm for Boolean circuits, our circuits have multiple ..."
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We investigate the complexity of uniform OR circuits and AND circuits of polynomialsize and depth. As their name suggests, OR circuits have OR gates as their computation gates, as well as the usual input, output and constant 0/1 gates. As is the norm for Boolean circuits, our circuits have
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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computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored. AMS subject classifications: 82P10, 11Y05, 68Q10. 1 Introduction One of the first results in the mathematics of computation, which underlies the subsequent development
Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
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Cited by 681 (1 self)
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It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard
Strengths and Weaknesses of quantum computing
 SIAM JOURNAL OF COMPUTATION
, 1997
"... Recently a great deal of attention has been focused on quantum computation following a ..."
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Cited by 386 (10 self)
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Recently a great deal of attention has been focused on quantum computation following a
LowPower CMOS Digital Design
 JOURNAL OF SOLIDSTATE CIRCUITS. VOL 27, NO 4. APRIL 1992 413
, 1992
"... Motivated by emerging batteryoperated applications that demand intensive computation in portable environments, techniques are investigated which reduce power consumption in CMOS digital circuits while maintaining computational throughput. Techniques for lowpower operation are shown which use the ..."
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Cited by 570 (20 self)
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Motivated by emerging batteryoperated applications that demand intensive computation in portable environments, techniques are investigated which reduce power consumption in CMOS digital circuits while maintaining computational throughput. Techniques for lowpower operation are shown which use
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
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Cited by 627 (44 self)
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Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized
Opportunistic Beamforming Using Dumb Antennas
 IEEE Transactions on Information Theory
, 2002
"... Multiuser diversity is a form of diversity inherent in a wireless network, provided by independent timevarying channels across the different users. The diversity benefit is exploited by tracking the channel fluctuations of the users and scheduling transmissions to users when their instantaneous cha ..."
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Cited by 801 (1 self)
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an additional role of opportunistic nulling of the interference created on users of adjacent cells. We discuss the design implications of implementing this scheme in a complete wireless system.
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