复杂性理论中单向函数的结合性、交换性、整体性和强不可逆性的强化和挑战
Enforcing and Defying Associativity, Commutativity, Totality, and Strong Noninvertibility for One-Way Functions in Complexity Theory
摘要：
Rabi和Sherman [RS97，RS93]证明了因子分解的困难性是存在单向函数的充分条件（即，p-时间可计算的，诚实的，p-时间不可逆的函数;本文是在最坏情况下的模型，而不是平均情况下的模型），是完全的，交换的，结合的，但不是强不可逆的。本文改进了P不等于NP的充分条件。更一般地说，在本文中，我们完全描述了哪些类型的单向函数与（普通的）单向函数站在一起或落在一起--等价地，与P不等于NP站在一起或落在一起。我们看看拉比和谢尔曼的开创性工作中使用的四个属性的代数性质的单向函数（见[RS97，RS93]）和随后的论文-强（不可逆性），整体性，交换性和结合性-对于每个属性，我们允许它被要求举行，要求失败，或``不在乎。在这个分类中，有3^4 = 81种可能的单向函数类型。我们证明，这81个功能负载类型的每一个站在或落在一起（平原）单向函数的存在。
英文摘要：
Rabi and Sherman [RS97,RS93] proved that the hardness of factoring is a sufficient condition for there to exist one-way functions (i.e., p-time computable, honest, p-time noninvertible functions; this paper is in the worst-case model, not the average-case model) that are total, commutative, and associative but not strongly noninvertible. In this paper we improve the sufficient condition to ``P does not equal NP.'' More generally, in this paper we completely characterize which types of one-way functions stand or fall together with (plain) one-way functions--equivalently, stand or fall together with P not equaling NP. We look at the four attributes used in Rabi and Sherman's seminal work on algebraic properties of one-way functions (see [RS97,RS93]) and subsequent papers--strongness (of noninvertibility), totality, commutativity, and associativity--and for each attribute, we allow it to be required to hold, required to fail, or ``don't care.'' In this categorization there are 3^4 = 81 potential types of one-way functions. We prove that each of these 81 feature-laden types stand or fall together with the existence of (plain) one-way functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
