In a STOC 1976 paper, Schaefer proved that it is PSPACE-complete to determine the winner of the so-called Maker-Breaker game on a given set system, even when every set has size at most 11. Since then, there has been no improvement on this result. We prove that the game remains ... more >>>

We investigate the number of pairwise comparisons sufficient to sort $n$ elements chosen from a linearly ordered set. This number is shown to be $\log_2(n!) + o(n)$ thus improving over the previously known upper bounds of the form $\log_2(n!) + \Theta(n)$. The new bound is achieved by the proposed group ... more >>>

A black-box (BB) reduction is a central proof technique in theoretical computer science. However, the limitations on BB reductions have been revealed for several decades, and the series of previous work gives strong evidence that we should avoid a nonadaptive BB reduction to base cryptography on NP-hardness (e.g., Akavia et ... more >>>