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Electronic Colloquium on Computational Complexity

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Reports tagged with TC0:
TR09-085 | 14th September 2009
Christoph Behle, Andreas Krebs, Stephanie Reifferscheid

An Approach to characterize the Regular Languages in TC0 with Linear Wires

Revisions: 1

We consider the regular languages recognized by weighted threshold circuits with a linear number of wires.
We present a simple proof to show that parity cannot be computed by such circuits.
Our proofs are based on an explicit construction to restrict the input of the circuit such that the value ... more >>>

TR11-095 | 22nd June 2011
Christoph Behle, Andreas Krebs, Klaus-Joern Lange, Pierre McKenzie

Low uniform versions of NC1

Revisions: 1

In the setting known as DLOGTIME-uniformity,
the fundamental complexity classes
$AC^0\subset ACC^0\subseteq TC^0\subseteq NC^1$ have several
robust characterizations.
In this paper we refine uniformity further and examine the impact
of these refinements on $NC^1$ and its subclasses.
When applied to the logarithmic circuit depth characterization of $NC^1$,
some refinements leave ... more >>>

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