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Communication Dans Un Congrès Année : 2022

Low-Latency Sliding Window Algorithms for Formal Languages

Résumé

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 $\mathcal{O}(\log n)$ 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 $n^{1/2-\epsilon}$ for any $\epsilon>0$, 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 $\mathcal{O}(1)$, $\mathcal{O}(\log\log n)$, and $\mathcal{O}(\log n)$.

Dates et versions

hal-03925398 , version 1 (05-01-2023)

Identifiants

Citer

Moses Ganardi, Louis Jachiet, Markus Lohrey, Thomas Schwentick. Low-Latency Sliding Window Algorithms for Formal Languages. 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022), Dec 2022, Chennai, India. ⟨10.4230/LIPIcs.FSTTCS.2022.38⟩. ⟨hal-03925398⟩
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