Abstract
The lower bound theory for circuits received an additional boost through algebraic techniques (in combination with probabilistic techniques) that go back to Razborov and Smolensky.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Valiant, Vazirani: NP is as easy as detecting unique solutions, Theoretical Computer Science 47 (1986), 85–93.
A. Razborov: Lower bounds on the size of bounded depth networks over a complete basis with logical addition, Mathematical Notes of the Academy of Sciences of the USSR 41 (1987), 333–338.
R. Smolensky: Algebraic methods in the theory of lower bounds for Boolean circuit complexity, Proceedings of the 19th Annual Symposium on Theory of Computing, ACM, 1979, 77-82.
N. Alon, J.H. Spencer: The Probabilistic Method, Wiley, 1992, Chapter 11.
R. Beigel: The polynomial method in circuit complexity, Structure in Complexity Theory Conference, IEEE, 1993.
M.L. Minsky, S.A. Papert: Perceptrons, MIT Press, 1969.
J. Aspnes, R. Beigel, M. Furst, S. Rudich: The expressive power of voting polynomials, Combinatorica 14 (1994) 135–148
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Schöning, U., Pruim, R. (1998). The Parity Function Again. In: Gems of Theoretical Computer Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60322-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-60322-8_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64352-1
Online ISBN: 978-3-642-60322-8
eBook Packages: Springer Book Archive