正则语言的随机滑动窗口算法
Randomized sliding window algorithms for regular languages
摘要：
滑动窗口算法接收符号流，并且必须在每个时刻输出仅取决于最后的$n$符号的特定值。如果算法是随机化的，则在每个时刻，它以最多$ε$的概率产生不正确的输出，这是恒定的误差界限。这项工作提出了一个更宽松的定义的正确性，这是参数化的错误界$ε$和故障率$ϕ$：一个随机滑动窗口算法是需要错误的概率最多$ε$在一部分的$1-ϕ$的所有时刻的输入流。本文的工作是对正则语言滑动窗口算法研究的继续。在以前的工作中，一个截分定理被证明是确定性算法：最佳的空间复杂度是常数，对数或线性的窗口大小。本文的主要结果涉及三个自然设置（失效率为零的随机算法和失效率有界的随机/确定性算法），并提供了空间复杂度类的自然语言理论刻画。
英文摘要：
A sliding window algorithm receives a stream of symbols and has to output at each time instant a certain value which only depends on the last $n$ symbols. If the algorithm is randomized, then at each time instant it produces an incorrect output with probability at most $ε$, which is a constant error bound. This work proposes a more relaxed definition of correctness which is parameterized by the error bound $ε$ and the failure ratio $ϕ$: A randomized sliding window algorithm is required to err with probability at most $ε$ at a portion of $1-ϕ$ of all time instants of an input stream. This work continues the investigation of sliding window algorithms for regular languages. In previous works a trichotomy theorem was shown for deterministic algorithms: the optimal space complexity is either constant, logarithmic or linear in the window size. The main results of this paper concerns three natural settings (randomized algorithms with failure ratio zero and randomized/deterministic algorithms with bounded failure ratio) and provide natural language theoretic characterizations of the space complexity classes.
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。
