2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1991)

San Juan, Puerto Rico

Oct. 1, 1991 to Oct. 4, 1991

ISBN: 0-8186-2445-0

pp: 662-669

D. Grigoriev , Dept. of Comput. Sci., Bonn Univ., Germany

M. Karpinski , Dept. of Comput. Sci., Bonn Univ., Germany

ABSTRACT

The authors design the first polynomial time (for an arbitrary and fixed field GF(q)) ( in , delta )-approximation algorithm for the number of zeros of arbitrary polynomial f(x/sub 1/. . . x/sub n/) over GF(q). It gives the first efficient method for estimating the number of zeros and nonzeros of multivariate polynomials over small finite fields other than GF(2) (like GF(3)), the case important for various circuit approximation techniques. The algorithm is based on the estimation of the number of zeros of an arbitrary polynomial f(x/sub 1/. . .,x/sub n/) over GF(q) in the function of the number m of its terms. The bounding ratio is proved to be m/sup (q-1)/log/sup q/.

INDEX TERMS

bounding ratio, polynomial time algorithm, approximation algorithm, zeros, arbitrary polynomials, multivariate polynomials, finite fields

CITATION

D. Grigoriev,
M. Karpinski,
"An approximation algorithm for the number of zeros or arbitrary polynomials over GF(q)",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 662-669, 1991, doi:10.1109/SFCS.1991.185433