We establish a relationship between the online mistake-bound model of learning and resource-bounded dimension. This connection is combined with the Winnow algorithm to obtain new results about the density of hard sets under adaptive reductions. This improves previous work of Fu (1995) and Lutz and Zhao (2000), and solves one ... more >>>

We use derandomization to show that sequences of positive $\pspace$-dimension -- in fact, even positive $\Delta^\p_k$-dimension
for suitable $k$ -- have, for many purposes, the full power of random oracles. For example, we show that, if $S$ is any binary sequence whose $\Delta^p_3$-dimension is positive, then $\BPP\subseteq \P^S$ and, moreover, ... more >>>

The PPSZ Algorithm presented by Paturi, Pudlak, Saks, and Zane in 1998 has the nice feature that the only satisfying solution of a uniquely satisfiable $3$-SAT formula can be found in expected running time at most $O(1.3071^n)$. Its bound degenerates when the number of solutions increases. In 1999, Schöning proved ... more >>>