The Time Required for Group Multiplication

Authors:
Philip M. Spira
Affiliations:
Stanford University, Department of Electrical Engineering, Stanford, California
Venue:
Journal of the ACM (JACM)
Year:
1969

Citing 2
Cited 10

On the Time Required to Perform Addition

Journal of the ACM (JACM)
On the Time Required to Perform Multiplication

Journal of the ACM (JACM)

Fast Addition of Large Integers

IEEE Transactions on Computers
The relationship between computational circuit complexity and radix

MVL '76 Proceedings of the sixth international symposium on Multiple-valued logic
On the computation time of certain classes of boolean functions

STOC '69 Proceedings of the first annual ACM symposium on Theory of computing
On the Time Necessary to Compute Switching Functions

IEEE Transactions on Computers
On the Addition of Binary Numbers

IEEE Transactions on Computers
Establishing lower bounds on algorithms: a survey

AFIPS '72 (Spring) Proceedings of the May 16-18, 1972, spring joint computer conference
Theory of computing in computer science education

AFIPS '72 (Spring) Proceedings of the May 16-18, 1972, spring joint computer conference
Computation Times of Arithmetic and Boolean Functions in (d, r) Circuits

IEEE Transactions on Computers
Parallel solution of recurrence problems

IBM Journal of Research and Development
On the computational complexity of finite functions and semigroup multiplication

Information Sciences: an International Journal

Quantified Score

Hi-index	0.03

Visualization

Abstract

Winograd has considered the time necessary to perform numerical addition and multiplication and to perform group multiplication by means of logical circuits consisting of elements each having a limited number of input lines and unit delay in computing their outputs. In this paper the same model as he employed is adopted, but a new lower bound is derived for group multiplication—the same as Winograd's for an Abelian group but in general stronger. Also a circuit is given to compute the multiplication which, in contrast to Winograd's, can be used for non-Abelian groups. When the group of interest is Abelian the circuit is at least as fast as his. By paralleling his method of application of his Abelian group circuit, it is possible also to lower the time necessary for numerical addition and multiplication.