We explain an asymmetric Prover-Delayer game which precisely characterizes proof size in tree-like Resolution. This game was previously described in a parameterized complexity context to show lower bounds for parameterized formulas and for the classical pigeonhole principle. The main point of this note is to show that the asymmetric game ... more >>>

We show that degree-$d$ block-symmetric polynomials in
$n$ variables modulo any odd $p$ correlate with parity
exponentially better than degree-$d$ symmetric
polynomials, if $n \ge c d^2 \log d$ and $d \in [0.995
\cdot p^t - 1,p^t)$ for some $t \ge 1$. For these
infinitely many degrees, our result ... more >>>

The study of locally testable codes (LTCs) has benefited from a number of nontrivial constructions discovered in recent years. Yet we still lack a good understanding of what makes a linear error correcting code locally testable and as a result we do not know what is the rate-limit of LTCs ... more >>>