In this paper, we prove the first super-polynomial and, in fact, exponential lower bound for the model of sum of read-once oblivious algebraic branching programs (ROABPs). In particular, we give an explicit polynomial such that any sum of ROABPs
(equivalently, sum of *ordered* set-multilinear branching programs, each with a ... more >>>

We study the problem of whether \emph{persistent} randomness is helpful for polynomial-time algorithms that only use \emph{logarithmic} space. In more detail, we consider the class $\searchBPLs$, of \emph{search}-problems that are solvable by a polynomial-time Probabilistic Logspace TMs with \emph{2-way} access (i.e., with multiple, as opposed to one-time, access) to a ... more >>>

While the existence of randomness extractors, both seeded and seedless, has been thoroughly studied for many sources of randomness, currently, very little is known regarding the existence of seedless condensers in many settings. Here, we prove several new results for seedless condensers in the context of three related classes of ... more >>>