Year: 2010
Type: preprint
Abstract: The work in this paper is to initiate a theory of testing monomials in multivariate polynomials. The central question is to ask whether a polynomial represented by certain economically compact structure has a multilinear monomial in its sum-product expansion. The complexity aspects of this problem and its variants are investigated with two folds of objectives. One is to understand how this problem relates to critical problems in complexity, and if so to what extent. The other is to exploit possibilities of applying algebraic properties of polynomials to the study of those problems. A series of results about $ΠΣΠ$ and $ΠΣ$ polynomials are obtained in this paper, laying a basis for further study along this line.
Source: arXiv (Cornell University)
Authors: Chen, Zhixiang, Fu, Bin
Institution: The University of Texas Rio Grande Valley
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2403492326