The complexity of testing monomials in multivariate polynomials

Authors:
Zhixiang Chen;Bin Fu
Affiliations:
Department of Computer Science, University of Texas-Pan American, Edinburg, TX;Department of Computer Science, University of Texas-Pan American, Edinburg, TX
Venue:
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Year:
2011

Citing 11
Cited 4

Perceptrons: expanded edition

Perceptrons: expanded edition
IP = PSPACE

Journal of the ACM (JACM)
On the learnability of Zn-DNF formulas (extended abstract)

COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Interactive proofs and the hardness of approximating cliques

Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems

Journal of the ACM (JACM)
Learning DNF in time

STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Derandomizing polynomial identity tests means proving circuit lower bounds

Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Faster Algebraic Algorithms for Path and Packing Problems

ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Finding paths of length k in O∗(2k) time

Information Processing Letters
Approximating multilinear monomial coefficients and maximum multilinear monomials in multivariate polynomials

COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Algorithms for testing monomials in multivariate polynomials

COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications

Algorithms for testing monomials in multivariate polynomials

COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Multivariate polynomial integration and differentiation are polynomial time inapproximable unless P=NP

FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Approximating multilinear monomial coefficients and maximum multilinear monomials in multivariate polynomials

Journal of Combinatorial Optimization
On testing monomials in multivariate polynomials

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

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 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.