A Dichotomy Theorem for Polynomial Evaluation
Computational Complexity
2009-12-15 v2
Abstract
A dichotomy theorem for counting problems due to Creignou and Hermann states that or any nite set S of logical relations, the counting problem #SAT(S) is either in FP, or #P-complete. In the present paper we show a dichotomy theorem for polynomial evaluation. That is, we show that for a given set S, either there exists a VNP-complete family of polynomials associated to S, or the associated families of polynomials are all in VP. We give a concise characterization of the sets S that give rise to "easy" and "hard" polynomials. We also prove that several problems which were known to be #P-complete under Turing reductions only are in fact #P-complete under many-one reductions.
Keywords
Cite
@article{arxiv.0902.2300,
title = {A Dichotomy Theorem for Polynomial Evaluation},
author = {Irénée Briquel and Pascal Koiran},
journal= {arXiv preprint arXiv:0902.2300},
year = {2009}
}