Document Open Access Logo

Visibly Pushdown Languages over Sliding Windows

Author Moses Ganardi

PDF
Thumbnail PDF

File

LIPIcs.STACS.2019.29.pdf
  • Filesize: 0.54 MB
  • 17 pages

Document Identifiers

Author Details

Moses Ganardi
  • Universität Siegen, Germany

Funding

The author is supported by the DFG project LO 748/13-1.

Cite As Get BibTex

Moses Ganardi. Visibly Pushdown Languages over Sliding Windows. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.STACS.2019.29

Abstract

We investigate the class of visibly pushdown languages in the sliding window model. A sliding window algorithm for a language L receives a stream of symbols and has to decide at each time step whether the suffix of length n belongs to L or not. The window size n is either a fixed number (in the fixed-size model) or can be controlled by an adversary in a limited way (in the variable-size model). The main result of this paper states that for every visibly pushdown language the space complexity in the variable-size sliding window model is either constant, logarithmic or linear in the window size. This extends previous results for regular languages.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming models
Keywords
  • visibly pushdown languages
  • sliding windows
  • rational transductions

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Rajeev Alur and P. Madhusudan. Visibly pushdown languages. In Proceedings of the 36th Annual ACM Symposium on Theory of Computing, Chicago, IL, USA, June 13-16, 2004, pages 202-211, 2004. URL: http://dx.doi.org/10.1145/1007352.1007390.
  2. 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
  3. 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
  4. Ajesh Babu, Nutan Limaye, Jaikumar Radhakrishnan, and Girish Varma. Streaming algorithms for language recognition problems. Theor. Comput. Sci., 494:13-23, 2013. URL: http://dx.doi.org/10.1016/j.tcs.2012.12.028.
  5. Vince Bárány, Christof Löding, and Olivier Serre. Regularity Problems for Visibly Pushdown Languages. In STACS 2006, 23rd Annual Symposium on Theoretical Aspects of Computer Science, Marseille, France, February 23-25, 2006, Proceedings, pages 420-431, 2006. URL: http://dx.doi.org/10.1007/11672142_34.
  6. Jean Berstel. Transductions and context-free languages, volume 38 of Teubner Studienbücher: Informatik. Teubner, 1979. Google Scholar
  7. Ahmed Bouajjani, Javier Esparza, and Oded Maler. Reachability Analysis of Pushdown Automata: Application to Model-Checking. In CONCUR '97: Concurrency Theory, 8th International Conference, Warsaw, Poland, July 1-4, 1997, Proceedings, pages 135-150, 1997. URL: http://dx.doi.org/10.1007/3-540-63141-0_10.
  8. Vladimir Braverman and Rafail Ostrovsky. Smooth Histograms for Sliding Windows. In Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science FOCS 2007, pages 283-293. IEEE Computer Society, 2007. Google Scholar
  9. Vladimir Braverman, Rafail Ostrovsky, and Carlo Zaniolo. Optimal sampling from sliding windows. J. Comput. Syst. Sci., 78(1):260-272, 2012. Google Scholar
  10. Dany Breslauer and Zvi Galil. Real-Time Streaming String-Matching. ACM Trans. Algorithms, 10(4):22:1-22:12, 2014. Google Scholar
  11. J Richard Büchi. Regular canonical systems. Archiv für mathematische Logik und Grundlagenforschung, 6(3-4):91-111, 1964. Google Scholar
  12. Raphaël Clifford, Allyx Fontaine, Ely Porat, Benjamin Sach, and Tatiana A. Starikovskaya. Dictionary Matching in a Stream. In Proceedings of ESA 2015, volume 9294 of Lecture Notes in Computer Science, pages 361-372. Springer, 2015. Google Scholar
  13. Raphaël Clifford, Allyx Fontaine, Ely Porat, Benjamin Sach, and Tatiana A. Starikovskaya. The k-mismatch problem revisited. In Proceedings of SODA 2016, pages 2039-2052. SIAM, 2016. Google Scholar
  14. Raphaël Clifford and Tatiana A. Starikovskaya. Approximate Hamming Distance in a Stream. In Proceedings of ICALP 2016, volume 55 of LIPIcs, pages 20:1-20:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. Google Scholar
  15. 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
  16. Emmanuel Filiot and Pierre-Alain Reynier. Transducers, logic and algebra for functions of finite words. SIGLOG News, 3(3):4-19, 2016. URL: http://dx.doi.org/10.1145/2984450.2984453.
  17. Nathanaël François, Frédéric Magniez, Michel de Rougemont, and Olivier Serre. Streaming Property Testing of Visibly Pushdown Languages. In Piotr Sankowski and Christos D. Zaroliagis, editors, 24th Annual European Symposium on Algorithms, ESA 2016, August 22-24, 2016, Aarhus, Denmark, volume 57 of LIPIcs, pages 43:1-43:17. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2016. URL: http://dx.doi.org/10.4230/LIPIcs.ESA.2016.43.
  18. Moses Ganardi. Visibly Pushdown Languages over Sliding Windows. Technical report, arXiv.org, 2018. URL: http://arxiv.org/abs/1812.11549.
  19. 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
  20. Moses Ganardi, Danny Hucke, Daniel König, Markus Lohrey, and Konstantinos Mamouras. Automata theory on sliding windows. Technical report, arXiv.org, 2018. URL: http://arxiv.org/abs/1702.04376.
  21. 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
  22. 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, August 27-31, 2018, Liverpool, UK, pages 15:1-15:15, 2018. URL: http://dx.doi.org/10.4230/LIPIcs.MFCS.2018.15.
  23. Seymour Ginsburg. The Mathematical Theory of Context-Free Languages. McGraw-Hill, Inc., New York, NY, USA, 1966. Google Scholar
  24. Seymour Ginsburg and Edwin H Spanier. Bounded ALGOL-like languages. Transactions of the American Mathematical Society, 113(2):333-368, 1964. Google Scholar
  25. Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. Recognizing Well-Parenthesized Expressions in the Streaming Model. SIAM J. Comput., 43(6):1880-1905, 2014. URL: http://dx.doi.org/10.1137/130926122.
  26. Rohit Parikh. On Context-Free Languages. J. ACM, 13(4):570-581, 1966. URL: http://dx.doi.org/10.1145/321356.321364.
  27. Christophe Reutenauer and Marcel Paul Schützenberger. Minimization of Rational Word Functions. SIAM J. Comput., 20(4):669-685, 1991. URL: http://dx.doi.org/10.1137/0220042.
  28. Andreas Weber and Reinhard Klemm. Economy of Description for Single-Valued Transducers. Inf. Comput., 118(2):327-340, 1995. URL: http://dx.doi.org/10.1006/inco.1995.1071.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact