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CONSTANT NUMBER PARALLEL MULTIPLIERS
"... A parallel multiplier for constant numbers is presented. The constant number is in Canonical Signed Digit (CSD) form and the other factor in two’s complement form. The result is obtained in two’s complement form. The design presented here is based on a special algorithm developed for the multipli ..."
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A parallel multiplier for constant numbers is presented. The constant number is in Canonical Signed Digit (CSD) form and the other factor in two’s complement form. The result is obtained in two’s complement form. The design presented here is based on a special algorithm developed
Scheduling on a Constant Number of Machines
"... Abstract. We consider the problem of scheduling independent jobs on a constant number of machines. We illustrate two important approaches for obtaining polynomial time approximation schemes for two different variants of the problem, more precisely the multiprocessorjob and the unrelatedmachines mo ..."
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Abstract. We consider the problem of scheduling independent jobs on a constant number of machines. We illustrate two important approaches for obtaining polynomial time approximation schemes for two different variants of the problem, more precisely the multiprocessorjob and the unrelated
SEQUENCES WITH CONSTANT NUMBER OF RETURN WORDS
"... Abstract. An infinite word has the property Rm if every factor has exactly m return words. Vuillon showed that R2 characterizes Sturmian words. We prove that a word satisfies Rm if its complexity function is (m − 1)n + 1 and if it contains no weak bispecial factor. These conditions are necessary for ..."
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Cited by 18 (5 self)
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Abstract. An infinite word has the property Rm if every factor has exactly m return words. Vuillon showed that R2 characterizes Sturmian words. We prove that a word satisfies Rm if its complexity function is (m − 1)n + 1 and if it contains no weak bispecial factor. These conditions are necessary for m = 3, whereas for m = 4 the complexity function need not be 3n + 1. A new class of words satisfying Rm is given. 1.
Regular Languages are Testable with a Constant Number of Queries
 SIAM Journal on Computing
, 1999
"... We continue the study of combinatorial property testing, initiated by Goldreich, Goldwasser and Ron in [7]. The subject of this paper is testing regular languages. Our main result is as follows. For a regular language L 2 f0; 1g and an integer n there exists a randomized algorithm which always acc ..."
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Cited by 90 (19 self)
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We continue the study of combinatorial property testing, initiated by Goldreich, Goldwasser and Ron in [7]. The subject of this paper is testing regular languages. Our main result is as follows. For a regular language L 2 f0; 1g and an integer n there exists a randomized algorithm which always accepts a word w of length n if w 2 L, and rejects it with high probability if w has to be modified in at least n positions to create a word in L. The algorithm queries ~ O(1=) bits of w. This query complexity is shown to be optimal up to a factor polylogarithmic in 1=. We also discuss testability of more complex languages and show, in particular, that the query complexity required for testing contextfree languages cannot be bounded by any function of . The problem of testing regular languages can be viewed as a part of a very general approach, seeking to probe testability of properties defined by logical means. 1
Determining the Number of Factors in Approximate Factor Models
, 2000
"... In this paper we develop some statistical theory for factor models of large dimensions. The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models. We propose a panel Cp criterion and show that the number of factors c ..."
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Cited by 538 (29 self)
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In this paper we develop some statistical theory for factor models of large dimensions. The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models. We propose a panel Cp criterion and show that the number of factors
On Bayesian analysis of mixtures with an unknown number of components
 INSTITUTE OF INTERNATIONAL ECONOMICS PROJECT ON INTERNATIONAL COMPETITION POLICY,&QUOT; COM/DAFFE/CLP/TD(94)42
, 1997
"... ..."
A Constant Number of Query Bits
"... rd to z, and then we may think of x as the decoding of z. There are two dual views of the Hadamard code, based on two different interpretations of i=1 x i y i . 1. View the x i as coefficients and the y i as variables. Then the codeword E(x) can be viewed as the linear function f x = i=1 x i y i ..."
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rd to z, and then we may think of x as the decoding of z. There are two dual views of the Hadamard code, based on two different interpretations of i=1 x i y i . 1. View the x i as coefficients and the y i as variables. Then the codeword E(x) can be viewed as the linear function f x = i=1 x i y i evaluated on all possible inputs. 2. View the y i as coefficients and the x i as variables. Then the codeword E(x) can be viewed as evaluating all possible linear functions (over GF (2) ) at the point x 2 f0; 1g . 1.2 The linearity test Given a string z 2 f0; 1g , we would like to test whether it is (close to) a codeword of the Hadamard code. As noted in Section 1.1, valid codewords can be viewed as linear functions f x . Likewise, we view z as a Boolean function f , and accessing the bit at location y 2 f0; 1g can be viewed as getting the value of f(y). For two strings x; y 2 f0; 1g , let x \Phi y 2 f0; 1g denote their bitwise exclusive or. The linearity test: Choose
Estimating the number of clusters in a dataset via the Gap statistic
, 2000
"... We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. kmeans or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference ..."
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Cited by 492 (1 self)
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We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. kmeans or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 822 (39 self)
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We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts
Results 1  10
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