论文标题
模块化电路中的中间问题令人满意
Intermediate problems in modular circuits satisfiability
论文作者
论文摘要
在ARXIV中：1710.08163已引入了布尔电路对任意有限代数的概括，并应用于素描P与NP-Complete的范围与NP-Complete的边界线，以使电路对代数模块化品种对代数的满意度。然而，nilpotent的问题（尚未证明是np- hard），但没有超努力的代数（已被证明是多项式时间）保持开放。 在本文中，我们提供了一个广泛的例子，位于这个灰色区域，并表明，在指数的时间假设和强大的大小假设下（说布尔式电路都需要指数级的许多模块化范围，以产生任何ARITY的波尔语结合），对这些代数的满意度），对这些代数的复杂性，$ pog和2^^2^^c^n n of nomential Compliendity nomeptiment conformition conformity coption countibles countible。 $ o（2^{c \ log^h n}）$，其中$ h $测量一个nilpotent代数无法成为超级努力。我们还概述了这些示例如何用作范式填充nilpotent and Supernilpotent Gap的范例。 鉴于布拉托夫（Bulatov）和祖克（Zhuk）显示了二分法，我们的例子令人惊讶地观察了电路可满足和约束满意度问题之间的自然牢固联系。
In arXiv:1710.08163 a generalization of Boolean circuits to arbitrary finite algebras had been introduced and applied to sketch P versus NP-complete borderline for circuits satisfiability over algebras from congruence modular varieties. However the problem for nilpotent (which had not been shown to be NP-hard) but not supernilpotent algebras (which had been shown to be polynomial time) remained open. In this paper we provide a broad class of examples, lying in this grey area, and show that, under the Exponential Time Hypothesis and Strong Exponential Size Hypothesis (saying that Boolean circuits need exponentially many modular counting gates to produce boolean conjunctions of any arity), satisfiability over these algebras have intermediate complexity between $Ω(2^{c\log^{h-1} n})$ and $O(2^{c\log^h n})$, where $h$ measures how much a nilpotent algebra fails to be supernilpotent. We also sketch how these examples could be used as paradigms to fill the nilpotent versus supernilpotent gap in general. Our examples are striking in view of the natural strong connections between circuits satisfiability and Constraint Satisfaction Problem for which the dichotomy had been shown by Bulatov and Zhuk.
