We prove optimal, up to an arbitrary > 0, inapproximability results for Max-Ek-Sat for k ≥ 3, maximizing the number of satisfied linear equations in an over-determined system of linear equations modulo a prime p and Set Splitting. As a consequence of these results we get improved lower bounds for the efficient approximability of many optimization problems studied previously. In particular, for Max-E2-Sat, Max-Cut, Max-di-Cut, and Vertex cover.

Pseudorandom generators are fundamental to many theoretical and applied aspects of computing. We show h o w to construct a pseudorandom generator from any oneway function. Since it is easy to construct a one-way function from a pseudorandom generator, this result shows that there is a pseudorandom generator i there is a one-way function.Warning: Essentially this paper has been published in SIAM Journal on Computing and is hence subject to copyright restrictions. It is for personal use only.

No abstract

No abstract

We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1))(log log n + k/2 + log k + log 1 ), where is the statistical difference between the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by Naor and Naor (our size bound is better as long as < 1/(k log n)). An additional advantage of our constructions is their simplicity.