Regular Languages in the Sliding Window Model
Year: 2025
Type: article
Abstract: We study the space complexity of the following problem: For a fixed regular language $L$, we receive a stream of symbols and want to test membership of a sliding window of size $n$ in $L$. For deterministic streaming algorithms we prove a trichotomy theorem, namely that the (optimal) space complexity is either constant, logarithmic or linear, measured in the window size $n$. Additionally, we provide natural language-theoretic characterizations of the space classes. We then extend the results to randomized streaming algorithms and we show that in this setting, the space complexity of any regular language is either constant, doubly logarithmic, logarithmic or linear. Finally, we introduce sliding window testers, which can distinguish whether a sliding window of size $n$ belongs to the language $L$ or has Hamming distance $> \epsilon n$ to $L$. We prove that every regular language has a deterministic (resp., randomized) sliding window tester that requires only logarithmic (resp., constant) space. Comment: 75 pages. This is the TheoretiCS journal version
Source: TheoretiCS
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Funder: Deutsche Forschungsgemeinschaft
Award: G7447426370
OpenAlex ID: W4408204085