By Topic

Reliable computation with noisy circuits and decision trees-a general n log n lower bound

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Reischuk, R. ; Tech. Hochschule Darmstadt, Germany ; Schmeltz, B.

Boolean circuits in which gates independently make errors with probability (at most) ε are considered. It is shown that the critical number crit(f) of a function f yields lower bound Ω(crit(f) log crit (f)) for the noisy circuit size. The lower bound is proved for an even stronger computational model, static Boolean decision trees with erroneous answers. A decision tree is static if the questions it asks do not depend on previous answers. The depth of such a tree provides a lower bound on the number of gates that depend directly on some input and hence on the size of a noisy circuit. Furthermore, it is shown that an Ω(n log n) lower bound holds for almost all Boolean n-input functions with respect to the depth of noisy dynamic decision trees. This bound is the best possible and implies that almost all n-input Boolean functions have noisy decision tree complexity Θ(n log n) in the static as well as in the dynamic case

Published in:

Foundations of Computer Science, 1991. Proceedings., 32nd Annual Symposium on

Date of Conference:

1-4 Oct 1991