函数的代数性质
Algebraic Properties for Selector Functions
摘要：
已知P-选择集的非确定性建议复杂度是精确线性的。关于P-选择集的确定性建议复杂度-即，多项式时间机器识别它们所需的Karp-Lipton建议的量-最佳当前上限是二次的[Ko，1983]，最佳当前下限是线性的[Hemaspaandra和Torenvliet，1996]。我们证明了每一个结合P-选择集都是可交换的，结合P-选择的。利用这一点，我们建立了一个代数充分条件的P-选择集有一个线性上界（从而将匹配现有的下界）的确定性建议的复杂性：如果所有的P-选择集是关联P-选择，那么P-选择集的确定性建议的复杂性是线性的。以前已知的最弱的充分条件是P=NP。我们还建立了相关结果的代数性质，并建议的复杂性，非确定性选择集。
英文摘要：
The nondeterministic advice complexity of the P-selective sets is known to be exactly linear. Regarding the deterministic advice complexity of the P-selective sets--i.e., the amount of Karp--Lipton advice needed for polynomial-time machines to recognize them in general--the best current upper bound is quadratic [Ko, 1983] and the best current lower bound is linear [Hemaspaandra and Torenvliet, 1996]. We prove that every associatively P-selective set is commutatively, associatively P-selective. Using this, we establish an algebraic sufficient condition for the P-selective sets to have a linear upper bound (which thus would match the existing lower bound) on their deterministic advice complexity: If all P-selective sets are associatively P-selective then the deterministic advice complexity of the P-selective sets is linear. The weakest previously known sufficient condition was P=NP. We also establish related results for algebraic properties of, and advice complexity of, the nondeterministically selective sets.
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