A two server private information retrieval (PIR) scheme
allows a user U to retrieve the i-th bit of an
n-bit string x replicated between two servers while each
server individually learns no information about i. The main
parameter of interest in a PIR scheme is its communication
complexity, namely the ... more >>>

We give tight lower bounds for the size of depth-3 circuits with limited bottom fanin computing symmetric Boolean functions. We show that any depth-3 circuit with bottom fanin $k$ which computes the Boolean function $EXACT_{n/(k+1)}^{n}$, has at least $(1+1/k)^{n+\O(\log n)}$ gates. We show that this lower bound is tight, by ... more >>>

We establish a 1-1 correspondence between Valiant's
character theory of matchgate/matchcircuit
and his signature theory of planar-matchgate/matchgrid,
thus unifying the two theories in expressibility.
Previously we had established a complete characterization
of general matchgates, in terms of a set of
useful Grassmann-Pl{\"u}cker identities.
With this correspondence,
we give a corresponding ... more >>>