We use this framework to construct HSGs for read-once CNFs and read-once CNFs with parities. For formulas on $n$ variables with density at least $\varepsilon$, our generators use $O(\log(n/\varepsilon))$ seed bits. This bound is optimal up to a constant factor. Applying the hitting reduction of Gopalan, Meka, Reingold, Trevisan, and ... more >>>

The Group Epimorphism Problem (GpEpi) asks, given two finite groups $G_1$ and $G_2$, whether there exists a surjective group homomorphism, or epimorphism, from $G_1$ to $G_2$. When the input groups are given by their multiplication (Cayley) tables, the problem admits a quasipolynomial-time algorithm in general, but little is known about ... more >>>

We introduce a new family of *parallel* time-bounded Kolmogorov complexity measures ($KP^t$).
A string $w$ has low $KP^t$ complexity if any individual bit of $w$ can be decompressed from a "short" description using "few" parallel processors within at most $t$ steps.

The definition of $KP^t$ uses Parallel Random Access Machines ... more >>>