Checking polynomial identities over any field: Towards a derandomization (1998)
| Venue: | In Proceedings of the 30th Annual ACM Symposium on Theory of Computing |
| Citations: | 19 - 0 self |
BibTeX
@INPROCEEDINGS{Lewin98checkingpolynomial,
author = {Daniel Lewin},
title = {Checking polynomial identities over any field: Towards a derandomization},
booktitle = {In Proceedings of the 30th Annual ACM Symposium on Theory of Computing},
year = {1998},
pages = {438--447},
publisher = {ACM Press}
}
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Abstract
We present a Monte Carlo algorithm for testing multivariate polynomial identities over any field using fewer random bits than other methods. To test if a polynomial P (x 1�::: �xn) is zero, our method uses Pn i=1dlog(di +1)erandom bits, where di is the degree of xi in P, to obtain any inverse polynomial error in polynomial time. The algorithm applies to polynomials given as a black box or in some implicit representation such as a straight-line program. Our method works by evaluating P at truncated formal power series representing square roots of irreducible polynomials over the field. This approach is similar to that of Chen and Kao [CK97], but with the advantage that the techniques are purely algebraic and apply to any field. We also prove a lower bound showing that the number of random bits used by our algorithm is essentially optimal in the black-box model. 1
