An elegant characterization of the complexity of constraint satisfaction problems has emerged in the form of the the algebraic dichotomy conjecture of [BKJ00]. Roughly speaking, the characterization asserts that a CSP $\Lambda$ is tractable if and only if there exist certain non-trivial operations known as polymorphisms to combine solutions to ... more >>>

We develop a new notion called {\it $(1-\epsilon)$-tester for a
set $M$ of functions} $f:A\to C$. A $(1-\epsilon)$-tester
for $M$ maps each element $a\in A$ to a finite number of
elements $B_a=\{b_1,\ldots,b_t\}\subset B$ in a smaller
sub-domain $B\subset A$ where for every $f\in M$ if
$f(a)\not=0$ then $f(b)\not=0$ for at ... more >>>

We exhibit $\epsilon$-biased distributions $D$
on $n$ bits and functions $f\colon \{0,1\}^n
\to \{0,1\}$ such that the xor of two independent
copies ($D+D$) does not fool $f$, for any of the
following choices:

1. $\epsilon = 2^{-\Omega(n)}$ and $f$ is in P/poly;

2. $\epsilon = 2^{-\Omega(n/\log n)}$ and $f$ is ... more >>>