We study the complexity of computing Boolean functions on general
Boolean domains by polynomial threshold functions (PTFs). A typical
example of a general Boolean domain is $\{1,2\}^n$. We are mainly
interested in the length (the number of monomials) of PTFs, with
their degree and weight being of secondary interest. We ... more >>>

We consider the problem of approximating the minmax value of a multiplayer game in strategic form. We argue that in 3-player games with 0-1 payoffs, approximating the minmax value within an additive constant smaller than $\xi/2$, where $\xi = \frac{3-\sqrt5}{2} \approx 0.382$, is not possible by a polynomial time algorithm. ... more >>>

We bound the minimum number $w$ of wires needed to compute any (asymptotically good) error-correcting code
$C:\{0,1\}^{\Omega(n)} \to \{0,1\}^n$ with minimum distance $\Omega(n)$,
using unbounded fan-in circuits of depth $d$ with arbitrary gates. Our main results are:

(1) If $d=2$ then $w = \Theta(n ({\log n/ \log \log n})^2)$.

(2) ... more >>>

We prove that any AC0 circuit augmented with {epsilon log^2 n}
MOD_m gates and with a MAJORITY gate at the output, require size
n^{Omega(log n)} to compute MOD_l, when l has a prime
factor not dividing m and epsilon is sufficiently small. We
also obtain ... more >>>

We obtain a characterization of ACC0 in terms of a natural class of
constant width circuits, namely in terms of constant width polynomial
size planar circuits. This is shown via a characterization of the
class of acyclic digraphs which can be embedded on a cylinder surface
in such a way ... more >>>

We consider the computational power of constant width polynomial
size cylindrical circuits and nondeterministic branching programs.
We show that every function computed by a Pi2 o MOD o AC0 circuit
can also be computed by a constant width polynomial size cylindrical
nondeterministic branching program (or cylindrical circuit) and
that ... more >>>