Steven Rudich

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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)
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)
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)
We consider the following adversarial situation. Let n, m and t be arbitrary integers, and let f : {0, 1}n &#x02192; {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)
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)
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)
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)
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)