Guest Column

Ben Volk
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引用次数: 0

Abstract

Algebraic Natural Proofs is a recent framework which formalizes the type of reasoning used for proving most lower bounds on algebraic computational models. This concept is similar to and inspired by the famous natural proofs notion of Razborov and Rudich [RR97] for boolean circuit lower bounds, but, unlike in the boolean case, it is an open problem whether this constitutes a barrier for proving super-polynomial lower bounds for strong models of algebraic computation. From an algebraic-geometric viewpoint, it is also related to basic questions in Geometric Complexity Theory (GCT), and from a meta-complexity theoretic viewpoint, it can be seen as an algebraic version of the MCSP problem. We survey the recent work around this concept which provides some evidence both for and against the existence of an algebraic natural proofs barrier, with an emphasis on the di erent viewpoints and the connections to other areas.
特约专栏
代数自然证明是一个最近的框架,它形式化了用于证明代数计算模型的大多数下界的推理类型。这个概念类似于Razborov和Rudich [RR97]关于布尔电路下界的著名的自然证明概念,并受到其启发,但是,与布尔情况不同,这是否构成证明代数计算强模型的超多项式下界的障碍是一个开放的问题。从代数-几何的角度来看,它也与几何复杂性理论(GCT)中的基本问题有关,从元复杂性理论的角度来看,它可以被视为MCSP问题的代数版本。我们调查了最近围绕这个概念的工作,它提供了一些支持和反对代数自然证明屏障存在的证据,重点是不同的观点和与其他领域的联系。
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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