In this paper, we study quantum OBDD model, it is a restricted version of read-once quantum branching programs, with respect to "width" complexity. It is known that the maximal gap between deterministic and quantum complexities is exponential. But there are few examples of functions with such a gap. We present ... more >>>

For any unsatisfiable CNF formula $F$ that is hard to refute in the Resolution proof system, we show that a gadget-composed version of $F$ is hard to refute in any proof system whose lines are computed by efficient communication protocols---or, equivalently, that a monotone function associated with $F$ has large ... more >>>

If $k<n$, can one express the majority of $n$ bits as the majority of at most $k$ majorities, each of at most $k$ bits? We prove that such an expression is possible only if $k = \Omega(n^{4/5})$. This improves on a bound proved by Kulikov and Podolskii, who showed that ... more >>>