P与RP的RAM等价物
The RAM equivalent of P vs. RP
摘要：
计算复杂性的一个基本问题是，在随机多项式时间（RP）模型下，利用随机性可解的问题的类是否大于在确定性多项式时间（P）中可解的问题的类。然而，这个问题只适用于图灵机，而不适用于随机存取机（RAM）。Simon（1981）能够证明，对于一个装备充分的随机存取机，非确定性地切换状态的能力并不需要任何计算优势。然而，在同一篇论文中，Simon描述了RAM模型下随机性的不同（可以说更自然）场景。根据Simon的提议，RAM程序能够执行伪函数$\textit{RAND}(y)$，而不是在每个执行步骤接收新的随机位，该伪函数返回$[0,y)$范围内的均匀分布的随机整数。在过去的30年里，以这种方式分配一个随机整数的能力是否比分配一个随机位的能力更强大仍然是一个悬而未决的问题。在本文中，我们关闭西蒙的开放问题，充分刻画类语言的识别在多项式时间的每个RAM的问题提出。我们表明，对于其中的一些，随机性不带来任何好处，但更有趣的是，我们表明，对其他人来说，它。
英文摘要：
One of the fundamental open questions in computational complexity is whether the class of problems solvable by use of stochasticity under the Random Polynomial time (RP) model is larger than the class of those solvable in deterministic polynomial time (P). However, this question is only open for Turing Machines, not for Random Access Machines (RAMs). Simon (1981) was able to show that for a sufficiently equipped Random Access Machine, the ability to switch states nondeterministically does not entail any computational advantage. However, in the same paper, Simon describes a different (and arguably more natural) scenario for stochasticity under the RAM model. According to Simon's proposal, instead of receiving a new random bit at each execution step, the RAM program is able to execute the pseudofunction $\textit{RAND}(y)$, which returns a uniformly distributed random integer in the range $[0,y)$. Whether the ability to allot a random integer in this fashion is more powerful than the ability to allot a random bit remained an open question for the last 30 years. In this paper, we close Simon's open problem, by fully characterising the class of languages recognisable in polynomial time by each of the RAMs regarding which the question was posed. We show that for some of these, stochasticity entails no advantage, but, more interestingly, we show that for others it does.
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。
