论文标题
甚至更快的CSAT算法超过〜超努力代数
Even faster algorithms for CSAT over~supernilpotent algebras
论文作者
论文摘要
在本文中，提出了两种算法解决电路的满足性问题，上面介绍了代数。第一个是确定性的，比Aichinger提出的以前最快的算法更快。第二个是具有线性时间复杂性的概率。以前的算法在有限组中的应用提供的时间复杂性通常低于以前最佳的时间（由földvári给出），而后者的应用会导致推论，如果G组在nilpotent是nilpotent的，则G组的电路满足性问题是可以在概率线性时间内触发的，或者如果GNP np np np np np np np np np np np np np np ni be nililpotent。通过将多项式上的多项式代数之间的方程式转换为有限磁场上的有限程度多项式方程，从而获得了结果。
In this paper two algorithms solving circuit satisfiability problem over supernilpotent algebras are presented. The first one is deterministic and is faster than fastest previous algorithm presented by Aichinger. The second one is probabilistic with linear time complexity. Application of the former algorithm to finite groups provides time complexity that is usually lower than in previously best (given by Földvári) and application of the latter leads to corollary, that circuit satisfiability problem for group G is either tractable in probabilistic linear time if G is nilpotent or is NP-complete if G fails to be nilpotent. The results are obtained, by translating equations between polynomials over supernilpotent algebras to bounded degree polynomial equations over finite fields.
