F. Bergadano, N.H. Bshouty, Stefano Varricchio

It has been shown in previous recent work that

multiplicity automata are predictable from multiplicity

and equivalence queries. In this paper we generalize

related notions in a matrix representation

and obtain a basis for the solution

of a number of open problems in learnability theory.

Membership queries are generalized ...
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Oded Goldreich, Dana Ron

In this paper, we consider the question of determining whether

a function $f$ has property $P$ or is $\e$-far from any

function with property $P$.

The property testing algorithm is given a sample of the value

of $f$ on instances drawn according to some distribution.

In some cases,

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Scott E. Decatur, Oded Goldreich, Dana Ron

In a variety of PAC learning models, a tradeoff between time and

information seems to exist: with unlimited time, a small amount of

information suffices, but with time restrictions, more information

sometimes seems to be required.

In addition, it has long been known that there are

concept classes ...
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Oded Goldreich, Ronitt Rubinfeld, Madhu Sudan

This is a revised version of work which has appeared

in preliminary form in the 36th FOCS, 1995.

Given a function $f$ mapping $n$-variate inputs from a finite field

$F$ into $F$,

we consider the task of reconstructing a list of all $n$-variate

degree $d$ polynomials which agree with $f$

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Rocco Servedio

We show that the class of monotone $2^{O(\sqrt{\log n})}$-term DNF

formulae can be PAC learned in polynomial time under the uniform

distribution. This is an exponential improvement over previous

algorithms in this model, which could learn monotone

$o(\log^2 n)$-term DNF, and is the first efficient algorithm

for ...
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Judy Goldsmith, Robert H. Sloan, Balázs Szörényi, György Turán

A theory, in this context, is a Boolean formula; it is

used to classify instances, or truth assignments. Theories

can model real-world phenomena, and can do so more or less

correctly.

The theory revision, or concept revision, problem is to

correct a given, roughly correct concept.

This problem is ...
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Jeffrey C. Jackson, Homin Lee, Rocco Servedio, Andrew Wan

We give an algorithm that with high probability properly learns random monotone t(n)-term

DNF under the uniform distribution on the Boolean cube {0, 1}^n. For any polynomially bounded function t(n) <= poly(n) the algorithm runs in time poly(n, 1/eps) and with high probability outputs an eps accurate monotone DNF ...
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Anindya De, Ilias Diakonikolas, Rocco Servedio

We initiate the study of \emph{inverse} problems in approximate uniform generation, focusing on uniform generation of satisfying assignments of various types of Boolean functions. In such an inverse problem, the algorithm is given uniform random satisfying assignments of an unknown function $f$ belonging to a class $\C$ of Boolean functions ... more >>>

Alexander A. Sherstov

The threshold degree of a Boolean function $f$ is the minimum degree of

a real polynomial $p$ that represents $f$ in sign: $f(x)\equiv\mathrm{sgn}\; p(x)$. In a seminal 1969

monograph, Minsky and Papert constructed a polynomial-size constant-depth

$\{\wedge,\vee\}$-circuit in $n$ variables with threshold degree $\Omega(n^{1/3}).$ This bound underlies ...
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Mahdi Cheraghchi, Piotr Indyk

For every fixed constant $\alpha > 0$, we design an algorithm for computing the $k$-sparse Walsh-Hadamard transform of an $N$-dimensional vector $x \in \mathbb{R}^N$ in time $k^{1+\alpha} (\log N)^{O(1)}$. Specifically, the algorithm is given query access to $x$ and computes a $k$-sparse $\tilde{x} \in \mathbb{R}^N$ satisfying $\|\tilde{x} - \hat{x}\|_1 \leq ... more >>>

Alexander A. Sherstov

The threshold degree of a Boolean function $f$ is the minimum degree of

a real polynomial $p$ that represents $f$ in sign: $f(x)\equiv\mathrm{sgn}\; p(x)$. Introduced

in the seminal work of Minsky and Papert (1969), this notion is central to

some of the strongest algorithmic and complexity-theoretic results for

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