Let $F$ be the field of $q$ elements, where $q=p^{\ell}$ for prime $p$. Informally speaking, a polynomial source is a distribution over $F^n$ sampled by low degree multivariate polynomials. In this paper, we construct extractors for polynomial sources over fields of constant size $q$ assuming $p \ll q$.

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An algorithmic meta theorem for a logic and a class $C$ of structures states that all problems expressible in this logic can be solved efficiently for inputs from $C$. The prime example is Courcelle's Theorem, which states that monadic second-order (MSO) definable problems are linear-time solvable on graphs of bounded ... more >>>

We construct an explicit disperser for affine sources over $\F_2^n$ with entropy $k=2^{\log^{0.9} n}=n^{o(1)}$. This is a polynomial time computable function $D:\F_2^n \ar \B$ such that for every affine space $V$ of $\F_2^n$ that has dimension at least $k$, $D(V)=\set{0,1}$. This improves the best previous construction of Ben-Sasson and Kopparty ... more >>>