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Electronic Colloquium on Computational Complexity

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All reports by Author Kristoffer Arnsfelt Hansen:

TR13-021 | 5th February 2013
Kristoffer Arnsfelt Hansen, Vladimir Podolskii

Polynomial threshold functions and Boolean threshold circuits

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 >>>

TR12-025 | 23rd March 2012
Kord Eickmeyer, Kristoffer Arnsfelt Hansen, Elad Verbin

Approximating the minmax value of 3-player games within a constant is as hard as detecting planted cliques

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 >>>

TR11-150 | 4th November 2011
Anna Gal, Kristoffer Arnsfelt Hansen, Michal Koucky, Pavel Pudlak, Emanuele Viola

Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates

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 >>>

TR06-079 | 12th June 2006
Kristoffer Arnsfelt Hansen

Lower Bounds for Circuits with Few Modular Gates using Exponential Sums

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 >>>

TR03-025 | 14th April 2003
Kristoffer Arnsfelt Hansen

Constant width planar computation characterizes ACC0

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 >>>

TR02-066 | 24th October 2002
Kristoffer Arnsfelt Hansen, Peter Bro Miltersen, V Vinay

Circuits on Cylinders

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 >>>

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