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Low-latency sliding window algorithms for regular and context-free languagesare studied, where latency refers to the worst-case time spent for a singlewindow update or query. For every regular language $L$ it is shown that thereexists a constant-latency solution that supports adding and removing symbolsindependently on both ends of the window (the so-called two-way variable-sizemodel). 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 lowerbound: 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-wayfixed-size model). The above mentioned results all refer to the unit-cost RAMmodel with logarithmic word size. For regular languages we also present arefined picture using word sizes $\mathcal{O}(1)$, $\mathcal{O}(\log\log n)$,and $\mathcal{O}(\log n)$.

Low-Latency Sliding Window Algorithms for Formal Languages