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- Boaz Barak, Oded Goldreich, +4 authors Ke Yang
- CRYPTO
- 2001

Informally, an <i>obfuscator</i> <i>O</i> is an (efficient, probabilistic) “compiler” that takes as input a program (or circuit) <i>P</i> and produces a new program <i>O</i>(<i>P</i>) that has the same functionality as <i>P</i> yet is “unintelligible” in some sense. Obfuscators, if they exist, would have a wide variety of… (More)

- Russell Impagliazzo, Steven Rudich
- STOC
- 1988

We present strong evidence that the implication, “if one-way permutations exist, then secure secret key agreement is possible”, is not provable by standard techniques. Since both sides of this implication are widely believed true in real life, to show that the implication is false requires a new model. We consider a world where all parties have… (More)

- Sampath Kannan, Moni Naor, Steven Rudich
- SIAM J. Discrete Math.
- 1988

How to represent a graph in memory is a fundamental data structuring question. In the usual representations of an <italic>n</italic>-node graph, the names of the nodes (i.e. integers from 1 to <italic>n</italic>) betray nothing about the graph itself. Indeed, the names (or labels) on the <italic>n</italic> nodes are just log<italic>n</italic> bit place… (More)

We present new results on the well-studied 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 first positive result known for learning general DNF in polynomial time in a nontrivial model.… (More)

- Alexander A. Razborov, Steven Rudich
- STOC
- 1994

We introduce the notion of natural proof. We argue that the known proofs of lower bounds on the complexity of explicit Boolean functions in non-monotone models fall within our definition of natural. We show based on a hardness assumption that natural proofs can’t prove superpolynomial lower bounds for general circuits. We show that the weaker class of… (More)

- Benny Chor, Oded Goldreich, Johan Hasted, Joel Freidmann, Steven Rudich, Roman Smolensky
- 26th Annual Symposium on Foundations of Computer…
- 1985

We consider the following adversarial situation. Let n, m and t be arbitrary integers, and let f : {0, 1}n → {0, 1}m be a function. An adversary, knowing the function f, sets t of the n input bits, while the rest (n-t input, bits) are chosen at random (independently and with uniform probability distribution) The adversary tries to prevent the… (More)

- David A. Mix Barrington, Richard Beigel, Steven Rudich
- computational complexity
- 1992

Define the MOD m -degree of a boolean functionF to be the smallest degree of any polynomialP, over the ring of integers modulom, such that for all 0–1 assignments $$\vec x$$ , $$F(\vec x) = 0$$ iff $$P(\vec x) = 0$$ . We obtain the unexpected result that the MOD m -degree of the OR ofN variables is $$O(\sqrt[\tau ]{N})$$ , wherer is the number of distinct… (More)

- James Aspnes, Richard Beigel, Merrick L. Furst, Steven Rudich
- Combinatorica
- 1991

We consider the problem of approximating a Boolean function ~ : {O, 1 }m ~ {O, 1} by an integer polynomial p of degree k. For us, a polynomial p(z) predicts the value of ~(z) if, whenever p(z) ~ O, ~(x) = 1, and whenever p(x) < 0, ~(o) = O. A low-degree polynomial p is a good approximator for .f if it predicts ~ at almost all points. Given a positive… (More)

- Noga Alon, Richard Beigel, Simon Kasif, Steven Rudich, Benny Sudakov
- SIAM J. Comput.
- 2002

We consider the problem of learning a matching (i.e., a graph in which all vertices have degree 0 or 1) in a model where the only allowed operation is to query whether a set of vertices induces an edge. This is motivated by a problem that arises in molecular biology. In the deterministic nonadaptive setting, we prove a ( 1 2 + o(1)) ( n 2 ) upper bound and… (More)

- Tapan K Chatterjee, Lynn L Stoll, +9 authors Neal L Weintraub
- Circulation research
- 2009

Adipose tissue depots originate from distinct precursor cells, are functionally diverse, and modulate disease processes in a depot-specific manner. However, the functional properties of perivascular adipocytes, and their influence on disease of the blood vessel wall, remain to be determined. We show that human coronary perivascular adipocytes exhibit a… (More)