For a finite set $\cal F$ of polynomials over a fixed finite prime field of size $p$ containing all polynomials $x^2 - x$, a Nullstellensatz proof of the unsolvability of the system
$$
f = 0\ ,\ \mbox{ all } f \in {\cal F}
$$
is a linear combination ... more >>>

Koch, Strassle, and Tan [SODA 2023], show that, under the randomized exponential time hypothesis, there is no distribution-free PAC-learning algorithm that runs in time $n^{\tilde O(\log\log s)}$ for the classes of $n$-variable size-$s$ DNF, size-$s$ Decision Tree, and $\log s$-Junta by DNF (that returns a DNF hypothesis). Assuming a natural ... more >>>

Cumulative memory---the sum of space used over the steps of a computation---is a fine-grained measure of time-space complexity that is a more accurate measure of cost for algorithms with infrequent spikes in memory usage in the context of technologies such as cloud computing that allow dynamic allocation and de-allocation of ... more >>>