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 >>>

We study batch verification in QMA query and communication complexity, where the goal is to understand how the resources needed to verify $m$ copies of a Boolean function $f$ depend on $m$. We give a general technique for proving lower bounds on the witness-query tradeoff needed to batch verify a ... more >>>

We show that several meta-complexity problems are NP-hard under randomized polynomial-time (half-Levin) reductions, and provably cannot be NP-hard under randomized Levin reductions, under the assumptions that
(cryptography): there exists a subexponentially-secure indistinguishability obfuscator in the sense of Barak et al. (JACM 2012), and
(proof complexity): there are no ... more >>>