Counting axioms do not polynomially simulate counting gates

R. Impagliazzo, Nathan Segerlind
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引用次数: 14

Abstract

We give a family of tautologies whose algebraic translations have constant-degree, polynomial size polynomial calculus refutations over Z/sub 2/, but which require superpolynomial size bounded-depth Frege proofs from Count/sub 2/ axioms. This gives a superpolynomial size separation of bounded-depth Frege plus mod 2 counting axioms from bounded-depth Frege plus parity gates. Combined with another result of the authors, it gives the first size (as opposed to degree) separation between the polynomial calculus and Nullstellensatz systems.
计数公理不多项式地模拟计数门
我们给出了一类重言式,它们的代数平移在Z/sub 2/上具有常次、多项式大小的多项式微积分反驳,但它们需要从Count/sub 2/公理中得到超多项式大小的有界深度的Frege证明。这给出了有界深度Frege加模2计数公理与有界深度Frege加奇偶校验门的超多项式大小分离。结合作者的另一个结果,它给出了多项式演算和Nullstellensatz系统之间的第一个大小(而不是度)分离。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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