Technical Report Series in Neural and Computational Learning

[john@dcs.rhbnc.ac.uk]

The European Community ESPRIT Working Group in Neural and Computational 
       Learning Theory (NeuroCOLT): two new reports available

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NeuroCOLT Technical Report NC-TR-94-010:
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Computational Complexity of Neural Networks: a Survey
by Pekka Orponen, Department of Computer Science, P. O. Box 26,
FIN-00014 University of Helsinki, Finland

Abstract:
We survey some of the central results in the complexity theory of discrete
neural networks, with pointers to the literature.
Our main emphasis is on the computational power
of various acyclic and cyclic network models, but we also discuss
briefly the complexity aspects of synthesizing networks from examples
of their behavior.


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NeuroCOLT Technical Report NC-TR-94-012:
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A Note on Testing the Resultant
by T. Lickteig Universit\"at Bonn and K. Meer RWTH Aachen
Germany

Abstract:
\def\C{\prime \kern -5pt C}          % Menge der komplexen Zahlen    : \C
In a recent paper Shub proposes to attack the complex $P_{\C} $ versus
$NP_{\C} $ problem by focussing on lower bounds on testing the resultant of
quadratic forms for zero. Taking up this question we show in the present
paper a lower bound of order $n^3$ for testing the resultant of $n$
homogeneous polynomials of degree 2 in $n$ unknowns to vanish.


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The Report NC-TR-94-010 can be accessed and printed as follows 

% ftp cscx.cs.rhbnc.ac.uk  (134.219.200.45)
Name: anonymous
password: your full email address
ftp> cd pub/neurocolt/tech_reports
ftp> binary
ftp> get nc-tr-94-010.ps.Z
ftp> bye
% zcat nc-tr-94-010.ps.Z | lpr -l


Likewise for NC-TR-94-012. Uncompressed versions of the postscript files have also been
left for anyone not having an uncompress facility.

A full list of the currently available Technical Reports in the Series is held in a file
`abstracts' in the same directory.

Best wishes
John Shawe-Taylor