The sensitivity of a Boolean function $f$ is the maximum, over all inputs $x$, of the number of sensitive coordinates of $x$ (namely the number of Hamming neighbors of $x$ with different $f$-value). The well-known sensitivity conjecture of Nisan (see also Nisan and Szegedy) states that every sensitivity-$s$ Boolean function ... more >>>

We make progress on some questions related to polynomial approximations of $\mathrm{AC}^0$. It is known, by works of Tarui (Theoret. Comput. Sci. 1993) and Beigel, Reingold, and Spielman (Proc. $6$th CCC 1991), that any $\mathrm{AC}^0$ circuit of size $s$ and depth $d$ has an $\varepsilon$-error probabilistic polynomial over the reals ... more >>>

The reversible pebble game is a combinatorial game played on rooted DAGs. This game was introduced by Bennett (1989) motivated by applications in designing space efficient reversible algorithms. Recently, Chan (2013) showed that the reversible pebble game number of any DAG is the same as its Dymond-Tompa pebble number and ... more >>>