We study the approximability of the \maxcsp problem over non-boolean domains, more specifically over $\{0,1,\ldots,q-1\}$ for some integer $q$. We obtain a approximation algorithm that achieves a ratio of $C(q) \cdot k/q^k$ for some constant $C(q)$ depending only on $q$. Further, we extend the techniques of Samorodnitsky and Trevisan to ... more >>>

We consider (uniform) reductions from computing a function f to the task of distinguishing the output of some pseudorandom generator G from uniform. Impagliazzo and Wigderson (FOCS `98, JCSS `01) and Trevisan and Vadhan (CCC `02, CC `07) exhibited such reductions for every function f in PSPACE. Moreover, their reductions ... more >>>

We prove an exponential lower bound for the size of constant depth multilinear arithmetic circuits computing either the determinant or the permanent (a circuit is called multilinear, if the polynomial computed by each of its gates is multilinear). We also prove a super-polynomial separation between the size of product-depth $d$ ... more >>>