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Low-Latency Sliding Window Algorithms for Formal Languages

Authors Moses Ganardi , Louis Jachiet , Markus Lohrey , Thomas Schwentick

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ACM Subject Classification
  • Theory of computation → Regular languages
  • Theory of computation → Grammars and context-free languages
  • Theory of computation → Streaming models
Keywords
  • Streaming algorithms
  • regular languages
  • context-free languages

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Abstract

Low-latency sliding window algorithms for regular and context-free languages are studied, where latency refers to the worst-case time spent for a single window update or query. For every regular language L it is shown that there exists a constant-latency solution that supports adding and removing symbols independently on both ends of the window (the so-called two-way variable-size model). We prove that this result extends to all visibly pushdown languages. For deterministic 1-counter languages we present a 𝒪(log n) latency sliding window algorithm for the two-way variable-size model where n refers to the window size. We complement these results with a conditional lower bound: there exists a fixed real-time deterministic context-free language L such that, assuming the OMV (online matrix vector multiplication) conjecture, there is no sliding window algorithm for L with latency n^(1/2-ε) for any ε > 0, even in the most restricted sliding window model (one-way fixed-size model). The above mentioned results all refer to the unit-cost RAM model with logarithmic word size. For regular languages we also present a refined picture using word sizes 𝒪(1), 𝒪(log log n), and 𝒪(log n).

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Moses Ganardi, Louis Jachiet, Markus Lohrey, and Thomas Schwentick. Low-Latency Sliding Window Algorithms for Formal Languages. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 38:1-38:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.FSTTCS.2022.38

Author Details

Moses Ganardi
  • Max Planck Institute for Software Systems, Kaiserslautern, Germany
Louis Jachiet
  • LTCI, Télécom Paris, Institut Polytechnique de Paris, France
Markus Lohrey
  • Universität Siegen, Germany
Thomas Schwentick
  • TU Dortmund University, Germany

Funding

  • Lohrey, Markus: Partly supported by the DFG project LO748/13-1.

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