Sliding Windows over Context-Free Languages

Authors Moses Ganardi, Artur Jez, Markus Lohrey



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Moses Ganardi
  • Universität Siegen, Germany
Artur Jez
  • University of Wrocław, Poland
Markus Lohrey
  • Universität Siegen, Germany

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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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References

  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 the 36th Annual ACM Symposium on Theory of Computing, STOC 2004, pages 202-211. ACM Press, 2004. Google Scholar
  3. Moses Ganardi, Danny Hucke, Daniel König, Markus Lohrey, and Konstantinos Mamouras. Automata theory on sliding windows. In Proceedings of the 35th Symposium on Theoretical Aspects of Computer Science, STACS 2018, volume 96 of LIPIcs, pages 31:1-31:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. Google Scholar
  4. Moses Ganardi, Danny Hucke, and Markus Lohrey. Querying regular languages over sliding windows. In Proceedings of the 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2016, volume 65 of LIPIcs, pages 18:1-18:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. Google Scholar
  5. Paweł Gawrychowski and Artur Jeż. Hyper-minimisation made efficient. In Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science, MFCS 2009, volume 5734 of Lecture Notes in Computer Science, pages 356-368. Springer, 2009. Google Scholar
  6. Seymour Ginsburg and Edwin H Spanier. Finite-turn pushdown automata. SIAM Journal on Control, 4(3):429-453, 1966. Google Scholar
  7. J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading, MA, 1979. Google Scholar
  8. Rohit Parikh. On context-free languages. Journal of the ACM, 13(4):570-581, 1966. Google Scholar
  9. Burchard von Braunmühl and Rutger Verbeek. Input-driven languages are recognized in log n space. In Proceedings of the 1983 International FCT-Conference, FCT 1983, volume 158 of Lecture Notes in Computer Science, pages 40-51. Springer, 1983. Google Scholar
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