We give the first time-space tradeoff lower bounds for Resolution proofs that apply to superlinear space. In particular, we show that there are formulas of size $N$ that have Resolution refutations of space and size each roughly $N^{\log_2 N}$ (and like all formulas have Resolution refutations of space $N$) for ... more >>>

To compare the complexity of the perfect matching problem for general graphs with that for planar graphs, one might try to come up with a reduction from the perfect matching problem to the planar perfect matching problem.
The obvious way to construct such a reduction is via a {\em planarizing ... more >>>

We study the problem of obtaining efficient, deterministic, black-box polynomial identity testing algorithms for depth-3 set-multilinear circuits (over arbitrary fields). This class of circuits has an efficient, deterministic, white-box polynomial identity testing algorithm (due to Raz and Shpilka), but has no known such black-box algorithm. We recast this problem as ... more >>>