Sliding Windows over Context-Free Languages

Ganardi, Moses; Jez, Artur; Lohrey, Markus

doi:10.4230/LIPIcs.MFCS.2018.15

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LIPIcs.MFCS.2018.15.pdf

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Document Identifiers

DOI: 10.4230/LIPIcs.MFCS.2018.15
URN: urn:nbn:de:0030-drops-95973

Author Details

Moses Ganardi

Universität Siegen, Germany

Artur Jez

University of Wrocław, Poland

Markus Lohrey

Universität Siegen, Germany

Cite AsGet BibTex

Moses Ganardi, Artur Jez, and Markus Lohrey. Sliding Windows over Context-Free Languages. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.MFCS.2018.15

Abstract

We study the space complexity of sliding window streaming algorithms that check membership of the window content in a fixed context-free language. For regular languages, this complexity is either constant, logarithmic or linear [Moses Ganardi et al., 2016]. We prove that every context-free language whose sliding window space complexity is log_2(n) - omega(1) must be regular and has constant space complexity. Moreover, for every c in N, c >= 1 we construct a (nondeterministic) context-free language whose sliding window space complexity is O(n^(1/c)) \ o(n^(1/c)). Finally, we give an example of a deterministic one-counter language whose sliding window space complexity is Theta((log n)^2).

Subject Classification

ACM Subject Classification

Theory of computation → Streaming models

Keywords

sliding windows
streaming algorithms
context-free languages

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