Given a non-negative real matrix $M$ of non-negative rank at least $r$, can we witness this fact by a small submatrix of $M$? While Moitra (SIAM J. Comput. 2013) proved that this cannot be achieved exactly, we show that such a witnessing is possible approximately: an $m\times n$ matrix always ... more >>>

The field of combinatorial reconfiguration studies search problems with a focus on transforming one feasible solution into another.

Recently, Ohsaka [STACS'23] put forth the Reconfiguration Inapproximability Hypothesis (RIH), which roughly asserts that there is some $\varepsilon>0$ such that given as input a $k$-CSP instance (for some constant $k$) over ... more >>>

We introduce the entangled quantum polynomial hierarchy $QEPH$ as the class of problems that are efficiently verifiable given alternating quantum proofs that may be entangled with each other. We prove $QEPH$ collapses to its second level. In fact, we show that a polynomial number of alternations collapses to just two. ... more >>>