We study two register arithmetic computation and skew arithmetic circuits. Our main results are the following:

(1) For commutative computations, we show that an exponential circuit size lower bound
for a model of 2-register straight-line programs (SLPs) which is a universal model
of computation (unlike width-2 algebraic branching programs that ... more >>>

Sensitivity, certificate complexity and block sensitivity are widely used Boolean function complexity measures. A longstanding open problem, proposed by Nisan and Szegedy, is whether sensitivity and block sensitivity are polynomially related. Motivated by the constructions of functions which achieve the largest known separations, we study the relation between 1-certificate complexity ... more >>>

We study an approximate version of $q$-query LDCs (Locally Decodable Codes) over the real numbers and prove lower bounds on the encoding length of such codes. A $q$-query $(\alpha,\delta)$-approximate LDC is a set $V$ of $n$ points in $\mathbb{R}^d$ so that, for each $i \in [d]$ there are $\Omega(\delta n)$ ... more >>>