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Automata Theory on Sliding Windows

Authors Moses Ganardi, Danny Hucke, Daniel König, Markus Lohrey, Konstantinos Mamouras

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  • regular languages
  • sliding window algorithms

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Abstract

In a recent paper we analyzed the space complexity of streaming algorithms whose goal is to decide membership of a sliding window to a fixed language. For the class of regular languages we proved a space trichotomy theorem: for every regular language the optimal space bound is either constant, logarithmic or linear. In this paper we continue this line of research: We present natural characterizations for the constant and logarithmic space classes and establish tight relationships to the concept of language growth. We also analyze the space complexity with respect to automata size and prove almost matching lower and upper bounds. Finally, we consider the decision problem whether a language given by a DFA/NFA admits a sliding window algorithm using logarithmic/constant space.

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Moses Ganardi, Danny Hucke, Daniel König, Markus Lohrey, and Konstantinos Mamouras. Automata Theory on Sliding Windows. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.STACS.2018.31

Author Details

Moses Ganardi
Danny Hucke
Daniel König
Markus Lohrey
Konstantinos Mamouras

References

  1. Charu C. Aggarwal. Data Streams - Models and Algorithms. Springer, 2007. Google Scholar
  2. Noga Alon, Yossi Matias, and Mario Szegedy. The space complexity of approximating the frequency moments. J. Comput. Syst. Sci., 58(1):137-147, 1999. 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. Theoretical Computer Science, 494:13-23, 2013. Google Scholar
  6. Ajesh Babu, Nutan Limaye, and Girish Varma. Streaming algorithms for some problems in log-space. In Proceedings of TAMC 2010, volume 6108 of Lecture Notes in Computer Science, pages 94-104. Springer, 2010. Google Scholar
  7. Vladimir Braverman. Sliding window algorithms. In Encyclopedia of Algorithms, pages 2006-2011. Springer, 2016. Google Scholar
  8. Vladimir Braverman and Rafail Ostrovsky. Smooth histograms for sliding windows. In Proceedings of 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. 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
  12. 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
  13. 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
  14. 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
  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. A. Policriti F. Parlamento and K. Rao. Witnessing differences without redundancies. Proceedings of the American Mathematical Society, 125(2):587-594, 1997. Google Scholar
  17. Philippe Flajolet and G. Nigel Martin. Probabilistic counting algorithms for data base applications. J. Comput. Syst. Sci., 31(2):182-209, 1985. Google Scholar
  18. Nathanaël François, Frédéric Magniez, Michel de Rougemont, and Olivier Serre. Streaming property testing of visibly pushdown languages. In Proceedings of ESA 2016, volume 57 of LIPIcs, pages 43:1-43:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. Google Scholar
  19. Moses Ganardi, Danny Hucke, Daniel König, Markus Lohrey, and Konstantinos Mamouras. Automata theory on sliding windows. Technical report, arXiv.org, 2018. URL: https://arxiv.org/abs/1702.04376.
  20. Moses Ganardi, Danny Hucke, and Markus Lohrey. Querying regular languages over sliding windows. In Proceedings of FSTTCS 2016, volume 65 of LIPIcs, pages 18:1-18:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. Google Scholar
  21. Pawel Gawrychowski, Dalia Krieger, Narad Rampersad, and Jeffrey Shallit. Finding the growth rate of a regular or context-free language in polynomial time. International Journal on Foundations of Computer Science, 21(4):597-618, 2010. Google Scholar
  22. 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
  23. Christian Konrad and Frédéric Magniez. Validating XML documents in the streaming model with external memory. ACM Trans. Database Syst., 38(4):27:1-27:36, 2013. Google Scholar
  24. Andreas Krebs, Nutan Limaye, and Srikanth Srinivasan. Streaming algorithms for recognizing nearly well-parenthesized expressions. In Proceedings of MFCS 2011, volume 6907 of Lecture Notes in Computer Science, pages 412-423. Springer, 2011. Google Scholar
  25. Michel Latteux. Langages á un compteur. Journal of Computer and System Sciences, 26(1):14-33, 1983. Google Scholar
  26. Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. Recognizing well-parenthesized expressions in the streaming model. SIAM J. Comput., 43(6):1880-1905, 2014. Google Scholar
  27. Philip M. Lewis II, Richard Edwin Stearns, and Juris Hartmanis. Memory bounds for recognition of context-free and context-sensitive languages. In Proceedings of SWCT (FOCS) 1965, pages 191-202. IEEE Computer Society, 1965. Google Scholar
  28. J. Ian Munro and Mike Paterson. Selection and sorting with limited storage. Theor. Comput. Sci., 12:315-323, 1980. Google Scholar
  29. Luc Segoufin and Cristina Sirangelo. Constant-memory validation of streaming XML documents against dtds. In Proceedings of ICDT 2007, volume 4353 of Lecture Notes in Computer Science, pages 299-313. Springer, 2007. Google Scholar
  30. Luc Segoufin and Victor Vianu. Validating streaming XML documents. In Proceedings of PODS 2002, pages 53-64. ACM, 2002. Google Scholar
  31. Richard Edwin Stearns, Juris Hartmanis, and Philip M. Lewis II. Hierarchies of memory limited computations. In Proceedings of SWCT (FOCS) 1965, pages 179-190. IEEE Computer Society, 1965. Google Scholar
  32. Howard Straubing. Finite semigroup varieties of the form V*D. Journal of Pure and Applied Algebra, 36:53-94, 1985. Google Scholar
  33. Andrew Szilard, Sheng Yu, Kaizhong Zhang, and Jeffrey Shallit. Characterizing regular languages with polynomial densities. In Proceedings of MFCS 1992, volume 629 of Lecture Notes in Computer Science, pages 494-503. Springer, 1992. Google Scholar
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