Centre for Discrete and Applicable Mathematics
	CDAM Research Report, LSE-CDAM-2003-21 December 2003

Abstract

We analyze Boolean functions using a recently proposed measure of their complexity. This complexity measure, motivated by the aim of relating the complexity of the functions with the generalization ability that can be obtained when the functions are implemented in feed-forward neural networks, is the sum of two components. The first of these is related to the `average sensitivity' of the function and the second is, in a sense, a measure of the `randomness' or lack of structure of the function. In this paper, we investigate the importance of using the second term in the complexity measure. We also explore the existence of very complex Boolean functions, considering, in particular, the symmetric Boolean functions.

A PDF file (184 kB) with the full contents of this report can be downloaded by clicking here.

Alternatively, if you would like to get a free hard copy of this report, please send the number of this report, LSE-CDAM-2003-21, together with your name and postal address to:

		CDAM Research Reports Series Centre for Discrete and Applicable Mathematics London School of Economics Houghton Street London WC2A 2AE, U.K.
		Phone: +44(0)-20-7955 7732. Fax: +44(0)-20-7955 6877. Email: info@maths.lse.ac.uk

		Introduction to the CDAM Research Report Series.
		CDAM Homepage.

Last changed: Wed 9 Feb 2005
For comments go to: http://www.maths.lse.ac.uk/webmaster.html