Querying Regular Languages over Sliding Windows

Authors Moses Ganardi, Danny Hucke, Markus Lohrey

Thumbnail PDF


  • Filesize: 488 kB
  • 14 pages

Document Identifiers

Author Details

Moses Ganardi
Danny Hucke
Markus Lohrey

Cite AsGet BibTex

Moses Ganardi, Danny Hucke, and Markus Lohrey. Querying Regular Languages over Sliding Windows. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


We study the space complexity of querying regular languages over data streams in the sliding window model. The algorithm has to answer at any point of time whether the content of the sliding window belongs to a fixed regular language. A trichotomy is shown: For every regular language the optimal space requirement is either in Theta(n), Theta(log(n)), or constant, where $n$ is the size of the sliding window.
  • streaming algorithms
  • regular languages
  • space complexity


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Charu C. Aggarwal. Data Streams - Models and Algorithms. Springer, 2007. Google Scholar
  2. Rajeev Alur and P. Madhusudan. Visibly pushdown languages. In Proceedings of STOC 2004, pages 202-211. ACM Press, 2004. Google Scholar
  3. Arvind Arasu and Gurmeet Singh Manku. Approximate counts and quantiles over sliding windows. In Proceedings of PODS 2004, pages 286-296. ACM, 2004. Google Scholar
  4. Brian Babcock, Mayur Datar, Rajeev Motwani, and Liadan O'Callaghan. Maintaining variance and k-medians over data stream windows. In Proceedings of PODS 2003, pages 234-243. ACM, 2003. Google Scholar
  5. Ajesh Babu, Nutan Limaye, Jaikumar Radhakrishnan, and Girish Varma. Streaming algorithms for language recognition problems. Theor. Comput. Sci., 494:13-23, 2013. Google Scholar
  6. Vladimir Braverman. Sliding window algorithms. In Encyclopedia of Algorithms, pages 2006-2011. Springer, 2016. Google Scholar
  7. Vladimir Braverman, Rafail Ostrovsky, and Carlo Zaniolo. Optimal sampling from sliding windows. J. Comput. Syst. Sci., 78(1):260-272, 2012. Google Scholar
  8. Michael S. Crouch, Andrew McGregor, and Daniel Stubbs. Dynamic graphs in the sliding-window model. In Proceedings of ESA 2013, volume 8125 of Lecture Notes in Computer Science, pages 337-348. Springer, 2013. Google Scholar
  9. Mayur Datar, Aristides Gionis, Piotr Indyk, and Rajeev Motwani. Maintaining stream statistics over sliding windows. SIAM J. Comput., 31(6):1794-1813, 2002. Google Scholar
  10. Manfred Droste, Werner Kuich, and Heiko Vogler. Handbook of Weighted Automata. Springer, 2009. Google Scholar
  11. Gudmund Skovbjerg Frandsen, Peter Bro Miltersen, and Sven Skyum. Dynamic word problems. J. ACM, 44(2):257-271, 1997. Google Scholar
  12. Lukasz Golab and M. Tamer Özsu. Processing sliding window multi-joins in continuous queries over data streams. In Proceedings of VLDB 2003, pages 500-511. Morgan Kaufmann, 2003. Google Scholar
  13. Markus Holzer and Barbara König. On deterministic finite automata and syntactic monoid size. Theor. Comput. Sci., 327(3):319-347, 2004. Google Scholar
  14. Howard Straubing. Finite Automata, Formal Logic, and Circuit Complexity. Birkhäuser, Boston, Basel, Berlin, 1994. Google Scholar