In this paper we consider the relationship between monomial-size and bit-complexity in Sums-of-Squares (SOS) in Polynomial Calculus Resolution over rationals (PCR/$\mathbb{Q}$). We show that there is a set of polynomial constraints $Q_n$ over Boolean variables that has both SOS and PCR/$\mathbb{Q}$ refutations of degree 2 and thus with only polynomially many monomials, but for which any SOS or PCR/$\mathbb{Q}$ refutation must have exponential bit-complexity, when the rational coefficients are represented with their reduced fractions written in binary.

翻译：在本文中,我们考虑了单体大小和比特复杂度之间的关系,即单体大小和比特复杂度(SOS)在单体微积分解对理性(PCR/$\mathbb ⁇ $)中的关系。我们发现,在布尔兰变量上存在一系列多面性制约,即SOS和PCR/$\mathbb ⁇ $对2级的反驳,因此只有多体数的单体数,但任何SOS或PCR/$\mathbb ⁇ $的反驳都必须具有指数性的比特复杂度,而当理性系数与以二进制写的减少的分数代表时。