In the last few days, a Denial of Service attack was launched on universities in Israel, leading the administrators of the Israel Academic network to block access to it from the global internet. Consequently, websites such as ECCC have been accessible only from within the Israeli and European academic networks.
It seems that this blocking was just removed, and we hope it will not be put back in the future.
Needless to say, deciding on such blocking is not in our control, but we do apologize for this disruption of service.
A depth-4 algebraic circuit with top fan-in $k$ and bottom fan-in $2$ is a circuit $\Phi$ of the form $\Phi = \sum_{i=1}^k \prod_{j=1}^{m_i} Q_{ij}$, where the polynomials $Q_{ij} \in \mathbb{K}[x_1, \ldots, x_n]$ have degree at most $2$.
The class of all such circuits is denoted by $\Sigma^k \Pi \Sigma ...
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For a Boolean function $f:\{0,1\}^n\to\{0,1\}$, the higher-order Boolean derivative $D_S f$ computes the parity of $f$ over each $S$-dimensional subcube. We prove that $D_S f\equiv 1$ exactly when $S$ is a maximal monomial support in the algebraic normal form of $f$. This correspondence motivates the derivative certificate depth $\Delta_\partial(f)$, defined ... more >>>
The hardness vs. randomness paradigm converts a function $f \colon \{0,1\}^n \rightarrow \{0,1\}$ that is hard for circuits of size $s$ into a pseudorandom generator (PRG) $G \colon \{0,1\}^d \to \{0,1\}^{s'}$ that fools circuits of size $s' = s'(s)$. In the application for derandomization, such as proofs of $\mathbf{BPP} = ... more >>>
