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21
Weakly Learning DNF and Characterizing Statistical Query Learning Using Fourier Analysis
 IN PROCEEDINGS OF THE TWENTYSIXTH ANNUAL SYMPOSIUM ON THEORY OF COMPUTING
, 1994
"... We present new results on the wellstudied problem of learning DNF expressions. We prove that an algorithm due to Kushilevitz and Mansour [13] can be used to weakly learn DNF formulas with membership queries with respect to the uniform distribution. This is the rst positive result known for learn ..."
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Cited by 130 (22 self)
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for learning general DNF in polynomial time in a nontrivial model. Our results should be contrasted with those of Kharitonov [12], who proved that AC 0 is not eciently learnable in this model based on cryptographic assumptions. We also present ecient learning algorithms in various models for the readk
On learning readksatisfyj DNF
 IN PROCEEDINGS OF THE SEVENTH ANNUAL ACM CONFERENCE ON COMPUTATIONAL LEARNING THEORY
, 1994
"... We study the learnability of ReadkSatisfyj (RkSj) DNF formulae. These are DNF formulae in which the maximal number of occurrences of a variable is bounded by k, and the number of terms satisfied by any assignment is at most j. We show that this class of functions is learnable in polynomial tim ..."
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Cited by 24 (9 self)
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We study the learnability of ReadkSatisfyj (RkSj) DNF formulae. These are DNF formulae in which the maximal number of occurrences of a variable is bounded by k, and the number of terms satisfied by any assignment is at most j. We show that this class of functions is learnable in polynomial
Mansour’s Conjecture is True for Random DNF Formulas
, 2010
"... In 1994, Y. Mansour conjectured that for every DNF formula on n variables with t terms there exists a polynomial p with t O(log(1/ǫ)) nonzero coefficients such that E x∈{0,1} n[(p(x) − f(x)) 2] ≤ ǫ. We make the first progress on this conjecture and show that it is true for randomly chosen DNF for ..."
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Cited by 7 (1 self)
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formulas and readonce DNF formulas. Our result yields the first polynomialtime query algorithm for agnostically learning these subclasses of DNF formulas with respect to the uniform distribution on {0, 1} n (for any constant error parameter). Applying recent work on sandwiching polynomials, our results
Learning kterm DNF Formulas with an Incomplete Membership Oracle
 In Proc. 5th Annu. Workshop on Comput. Learning Theory
, 1992
"... We consider the problem of learning kterm DNF formulas using equivalence queries and incomplete membership queries as defined by Angluin and Slonim. We demonstrate that this model can be applied to nonmonotone classes. Namely, we describe a polynomialtime algorithm that exactly identifies a k t ..."
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Cited by 12 (1 self)
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We consider the problem of learning kterm DNF formulas using equivalence queries and incomplete membership queries as defined by Angluin and Slonim. We demonstrate that this model can be applied to nonmonotone classes. Namely, we describe a polynomialtime algorithm that exactly identifies a k
Efficient ReadRestricted Monotone CNF/DNF Dualization by Learning with Membership Queries
, 1998
"... We consider exact learning monotone CNF formulas in which each variable appears at most some constant k times ("readk" monotone CNF). Let ..."
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Cited by 23 (1 self)
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We consider exact learning monotone CNF formulas in which each variable appears at most some constant k times ("readk" monotone CNF). Let
Pseudorandomness for Width 2 Branching Programs
"... Recently Bogdanov and Viola (FOCS 2007) and Lovett (ECCC07) constructed pseudorandom generators that fool degree k polynomials over F2 for an arbitrary constant k. We show that such generators can also be used to fool branching programs of width 2 and polynomial length that read k bits of inputs at ..."
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Cited by 5 (1 self)
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Recently Bogdanov and Viola (FOCS 2007) and Lovett (ECCC07) constructed pseudorandom generators that fool degree k polynomials over F2 for an arbitrary constant k. We show that such generators can also be used to fool branching programs of width 2 and polynomial length that read k bits of inputs
On the Readability of Monotone Boolean Formulae
, 2009
"... Golumbic et al. [Discrete Applied Mathematics 154(2006) 14651477] defined the readability of a monotone Boolean function f to be the minimum integer k such that there exists an ∧ − ∨formula equivalent to f in which each variable appears at most k times. They asked whether there exists a polynomia ..."
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Cited by 6 (0 self)
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polynomialtime algorithm, which given a monotone Boolean function f, in CNF or DNF form, checks whether f is a readk function, for a fixed k. In this paper, we paratially answer this question already for k = 2 by showing that it is NPhard to decide if a given monotone formula represents a read
Exact Learning of subclasses of CDNF formulas with membership queries
, 1996
"... . We consider the exact learnability of subclasses of Boolean formulas from membership queries alone. We show how to combine known learning algorithms that use membership and equivalence queries to obtain new learning results only with memberships. In particular we show the exact learnability of rea ..."
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Cited by 1 (1 self)
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of readk monotone CDNF formulas, Sat k O(log n)CDNF, and O( p log n)size CDNF from membership queries only. 1 Introduction Learning DNF formulas has been one of the most attractive and tantalizing problems since the seminal paper of Valiant [Val84]. Although many results in the literature give
Cryptographic Primitives Based on Hard Learning Problems
, 1994
"... this paper, we give results in the reverse direction by showing how to construct several cryptographic primitives based on certain assumptions on the difficulty of learning. In doing so, we develop further a line of thought introduced by Impagliazzo and Levin [6]. As we describe, standard definition ..."
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Cited by 105 (4 self)
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benefits of this line of research is that as "simple" function classes (for instance, DNF formulae) continue to elude efficient learning, our belief in the intractability of learning such classes increases, and we can exploit this intractability to obtain simpler cryptographic primitives. In add...
Learning, Cryptography, and the Average Case
, 2010
"... This thesis explores problems in computational learning theory from an averagecase perspective. Through this perspective we obtain a variety of new results for learning theory and cryptography. Several major open questions in computational learning theory revolve around the problem of efficiently l ..."
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formulas and readk DNF formulas. Our result yields the first polynomialtime query algorithm for agnostically learning these subclasses of DNF formulas with respect to the uniform distribution on {0, 1} n (for any constant error parameter and constant k). Applying
Results 1  10
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21