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Let $m = 1 + \log \ell$. Identify a hash function $h \colon \{0, 1\}^k \to \{0, 1\}^m$ with its $n$-bit truth table $h \in \{0, 1\}^n$ where $n = m \cdot 2^k$. Our hash family $\mathcal{H} \subseteq \{0, 1\}^n$ consists of an $\varepsilon$-biased set for a suitable $\varepsilon = \ell^{-\Theta(k)}$. Explicit constructions of such a hash family are known with ...


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The Perfect Matching problem was "almost" derandomized in 2016 [1]: there is a deterministic algorithm requiring "only" quaispolynomial resources, namely $n^{\mathcal O(\log n)}$ for the bipartite case and $n^{\mathcal O(\log^2n)}$ for the general case (in 2017 [2]). Although Edmonds gave a polynomial-time algorithm for perfect matching, ...


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