Constant depth circuits, Fourier transform, and learnability

Nathan Linial*, Yishay Mansour, Noam Nisan

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

68 Scopus citations

Abstract

Boolean functions in ACO are studied using the harmonic analysis of the cube. The main result is that an ACO Boolean function has almost all of its power spectrum on the low-order coefficients. This result implies the following properties of functions in ACO: functions in ACO have low average sensitivity; they can be approximated well by a real polynomial of low degree; they cannot be pseudorandom function generators and their correlation with any polylog-wise independent probability distribution is small. An O(npolylog (n))-time algorithm for learning functions in ACO is obtained. The algorithm observes the behavior of an ACO function on O(npolylog (n)) randomly chosen inputs and derives a good approximation for the Fourier transform of the function. This allows it to predict with high probability the value of the function on other randomly chosen inputs.

Original languageAmerican English
Title of host publicationAnnual Symposium on Foundations of Computer Science (Proceedings)
PublisherPubl by IEEE
Pages574-579
Number of pages6
ISBN (Print)0818619821, 9780818619823
DOIs
StatePublished - 1989
Externally publishedYes
Event30th Annual Symposium on Foundations of Computer Science - Research Triangle Park, NC, USA
Duration: 30 Oct 19891 Nov 1989

Publication series

NameAnnual Symposium on Foundations of Computer Science (Proceedings)
ISSN (Print)0272-5428

Conference

Conference30th Annual Symposium on Foundations of Computer Science
CityResearch Triangle Park, NC, USA
Period30/10/891/11/89

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