Proceedings 32nd Annual Symposium of Foundations of Computer Science (1991)
San Juan, Puerto Rico
Oct. 1, 1991 to Oct. 4, 1991
D. Grigoriev , Dept. of Comput. Sci., Bonn Univ., Germany
M. Karpinski , Dept. of Comput. Sci., Bonn Univ., Germany
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/.
bounding ratio, polynomial time algorithm, approximation algorithm, zeros, arbitrary polynomials, multivariate polynomials, finite fields
D. Grigoriev and M. Karpinski, "An approximation algorithm for the number of zeros or arbitrary polynomials over GF(q),"  Proceedings 32nd Annual Symposium of Foundations of Computer Science(FOCS), San Juan, Puerto Rico, 1991, pp. 662-669.