|
| This Article | ||
| | ||
| Share | ||
| Bibliographic References | ||
| Add to: | ||
 Digg  Furl  Spurl  Blink  Simpy  Google  Del.icio.us  Y!MyWeb | ||
| Search | ||
| ||
31st Annual Symposium on Foundations of Computer Science (FOCS 1990)
St. Louis, MO, USA
October 22-October 24
ISBN: 0-8186-2082-X
| ASCII Text | x | ||
| J. Bruck, R. Smolensky, "Polynomial threshold functions, AC functions and spectrum norms," Foundations of Computer Science, IEEE Annual Symposium on, pp. 632-641 vol.2, 31st Annual Symposium on Foundations of Computer Science (FOCS 1990), 1990. | |||
| BibTex | x | ||
| @article{ 10.1109/FSCS.1990.89585, author = {J. Bruck and R. Smolensky}, title = {Polynomial threshold functions, AC functions and spectrum norms}, journal ={Foundations of Computer Science, IEEE Annual Symposium on}, volume = {0}, year = {1990}, isbn = {0-8186-2082-X}, pages = {632-641 vol.2}, doi = {http://doi.ieeecomputersociety.org/10.1109/FSCS.1990.89585}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - CONF JO - Foundations of Computer Science, IEEE Annual Symposium on TI - Polynomial threshold functions, AC functions and spectrum norms SN - 0-8186-2082-X SP632 EP641 vol.2 A1 - J. Bruck, A1 - R. Smolensky, PY - 1990 KW - spectral representation KW - AC functions KW - spectrum norms KW - polynomial-threshold functions KW - harmonic analysis KW - Boolean function VL - 0 JA - Foundations of Computer Science, IEEE Annual Symposium on ER - | |||
The class of polynomial-threshold functions is studied using harmonic analysis, and the results are used to derive lower bounds related to AC/sup 0/ functions. A Boolean function is polynomial threshold if it can be represented as a sign function of a sparse polynomial (one that consists of a polynomial number of terms). The main result is that polynomial-threshold functions can be characterized by means of their spectral representation. In particular, it is proved that a Boolean function whose L/sub 1/ spectral norm is bounded by a polynomial in n is a polynomial-threshold function, and that a Boolean function whose L/sub infinity //sup -1/ spectral norm is not bounded by a polynomial in n is not a polynomial-threshold function. Some results for AC/sup 0/ functions are derived.
Index Terms:
spectral representation, AC functions, spectrum norms, polynomial-threshold functions, harmonic analysis, Boolean function
Citation:
J. Bruck, R. Smolensky, "Polynomial threshold functions, AC functions and spectrum norms," focs, pp.632-641 vol.2, 31st Annual Symposium on Foundations of Computer Science (FOCS 1990), 1990
Usage of this product signifies your acceptance of the Terms of Use.