Randomized Sliding Window Algorithms for Regular Languages

Authors Moses Ganardi, Danny Hucke, Markus Lohrey

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Moses Ganardi
  • Universität Siegen, Germany
Danny Hucke
  • Universität Siegen, Germany
Markus Lohrey
  • Universität Siegen, Germany

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Moses Ganardi, Danny Hucke, and Markus Lohrey. Randomized Sliding Window Algorithms for Regular Languages. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 127:1-127:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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 epsilon, which is a constant error bound. This work proposes a more relaxed definition of correctness which is parameterized by the error bound epsilon and the failure ratio phi: a randomized sliding window algorithm is required to err with probability at most epsilon at a portion of 1-phi 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming models
  • sliding windows
  • regular languages
  • randomized complexity


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