Quantified conflict-driven clause learning (QCDCL) is one of the main approaches for solving quantified Boolean formulas (QBF). We formalise and investigate several versions of QCDCL that include cube learning and/or pure-literal elimination, and formally compare the resulting solving models via proof complexity techniques. Our results show that almost all of ... more >>>

Hypercontractive inequalities for real-valued functions over the Boolean cube play an important role in theoretical computer science. In this work, we prove a hypercontractive inequality for matrix-valued functions defined over large alphabets, generalizing the result of Ben-Aroya, Regev, de Wolf (FOCS'08) for the Boolean alphabet. To obtain our result we ... more >>>

A distribution is called $m$-grained if each element appears with probability that is an integer multiple of $1/m$.
We prove that, for any constant $c<1$, testing whether a distribution over $[\Theta(m)]$ is $m$-grained requires $\Omega(m^c)$ samples.

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