Monomial size vs. Bit-complexity in Sums-of-Squares and Polynomial Calculus

In this paper we consider the relationship between monomial-size and bit-complexity in Sums-of-Squares (SOS) in Polynomial Calculus Resolution over rationals ({\text{PCR}}/\mathbb{Q}). We show that there is a set of polynomial constraints Q n over Boolean variables that has both SOS and {\text{PCR}}...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 7
Main Author: Hakoniemi, Tuomas
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
Calculus
Computer science
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we consider the relationship between monomial-size and bit-complexity in Sums-of-Squares (SOS) in Polynomial Calculus Resolution over rationals ({\text{PCR}}/\mathbb{Q}). We show that there is a set of polynomial constraints Q n over Boolean variables that has both SOS and {\text{PCR}}/\mathbb{Q} refutations of degree 2 and thus with only polynomially many monomials, but for which any SOS or {\text{PCR}}/\mathbb{Q} refutation must have exponential bit-complexity, when the rational coefficients are represented with their reduced fractions written in binary.
DOI:10.1109/LICS52264.2021.9470545