Let $\Sigma$ be an alphabet and $\mu$ be a distribution on $\Sigma^k$ for some $k \geq 2$. Let $\alpha > 0$ be the minimum probability of a tuple in the support of $\mu$ (denoted by $supp(\mu)$). Here, the support of $\mu$ is the set of all tuples in $\Sigma^k$ that ... more >>>

In this paper we study functions on the Boolean hypercube that have the property that after applying certain random restrictions, the restricted function is correlated to a linear function with non-negligible probability. If the given function is correlated with a linear function then this property clearly holds. Furthermore, the property ... more >>>

The proof complexity of Quantified Boolean Formulas (QBF) relates to both QBF solving and OBF certification. One method to p-simulate a QBF proof system is by formalising the soundness of its strategy extraction in propositional logic. In this work we illustrate how to use extended QBF Frege to simulate LD-Q(Drrs)-Res, ... more >>>