csp与连通性:幂等右拟群的P/NP二分法

Robert W. McGrail, James M. Belk, Solomon Garber, J. Wood, Benjamin Fish
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引用次数: 2

摘要

在20世纪90年代,Jeavons证明了每一个有限代数对应于一类约束满足问题。Vardi后来推测幂等代数表现出P/NP二分性:这门课中的每一个非NP完全代数都必须是可处理的。这里我们讨论了在Cayley图中可跟踪性是如何对应于连通性的。特别地,我们证明了有限幂等右拟群的二分类遵循一个很强的连通性概念。此外,P/NP隶属关系是一阶公理化的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
CSPs and Connectedness: P/NP Dichotomy for Idempotent, Right Quasigroups
In the 1990's, Jeavons showed that every finite algebra corresponds to a class of constraint satisfaction problems. Vardi later conjectured that idempotent algebras exhibit P/NP dichotomy: Every non NP-complete algebra in this class must be tractable. Here we discuss how tractability corresponds to connectivity in Cayley graphs. In particular, we show that dichotomy in finite idempotent, right quasi groups follows from a very strong notion of connectivity. Moreover, P/NP membership is first-order axiomatizable in involutory quandles.
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