Abstract
Algebraic techniques are used to prove that any circuit constructed with MOD q gates that computes the AND function must use Ω(n) gates at the first level. This constitutes the first non-trivial lower bound on the circuit size required to compute AND with MOD q gates that is valid for arbitrary q.
This article was processed using the LATEX macro package with LMAMULT style
Preview
Unable to display preview. Download preview PDF.
References
Barrington, D. A. Mix, Straubing, H. and Thérien, D., Non-uniform automata over groups, Information and Computation 89, 2, (1990) 109–132.
Euler, L., Opusc. analytics, Vol. 2 (1785), p. 241.
Furst, M., Saxe, J. B. and Sipser, M., Parity, circuits and the polynomial-time hierarchy, Math. Systems Theory 18 (1984), 13–27.
Smolensky, R., Algebraic methods in the theory of lower bounds for boolean circuit complexity, Proc. 19th ACM STOC (1987), 77–82.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Thérien, D. (1992). Circuits constructed with MOD q gates cannot compute AND in sublinear size. In: Simon, I. (eds) LATIN '92. LATIN 1992. Lecture Notes in Computer Science, vol 583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023851
Download citation
DOI: https://doi.org/10.1007/BFb0023851
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55284-0
Online ISBN: 978-3-540-47012-0
eBook Packages: Springer Book Archive