It is well known that there is a sharp density threshold for a random r-SAT formula to be satisfiable, and a similar, smaller, threshold for it to be satisfied by the pure literal ...
In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edge...
A simple first moment argument shows that in a randomly chosen k-SAT formula with m clauses over n boolean variables, the fraction of satisfiable clauses is 1−2−k +o(1) as m/...
In this work we give the first deterministic extractors from a constant number of weak sources whose entropy rate is less than 1/2. Specifically, for every > 0 we give an expl...
We consider random 3CNF formulas with n variables and m clauses. It is well known that when m > cn (for a sufficiently large constant c), most formulas are not satisfiable. How...