Document Open Access Logo

Trading Determinism for Time in Space Bounded Computations

Authors Vivek Anand T Kallampally, Raghunath Tewari

PDF

File

Thumbnail PDF
PDF
LIPIcs.MFCS.2016.10.pdf
  • Filesize: 461 kB
  • 13 pages

Document Identifiers

Subject Classification

Keywords
  • space complexity
  • unambiguous computations
  • Savitch's Theorem

Metrics

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

Abstract

Savitch showed in 1970 that nondeterministic logspace (NL) is contained in deterministic O(log^2(n)) space but his algorithm requires quasipolynomial time. The question whether we can have a deterministic algorithm for every problem in NL that requires polylogarithmic space and simultaneously runs in polynomial time  was left open. 
		
In this paper we give a partial solution to this problem and show that for every language in NL there exists an unambiguous nondeterministic algorithm that requires O(log^2(n)) space and simultaneously runs in polynomial time.

Cite As Get BibTex

Vivek Anand T Kallampally and Raghunath Tewari. Trading Determinism for Time in Space Bounded Computations. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.MFCS.2016.10

Author Details

Vivek Anand T Kallampally
Raghunath Tewari

References

  1. Eric Allender, Klaus Reinhardt, and Shiyu Zhou. Isolation, matching, and counting: Uniform and nonuniform upper bounds. Journal of Computer and System Sciences, 59:164-181, 1999. Google Scholar
  2. Carme Àlvarez and Birgit Jenner. A very hard log-space counting class. Theoretical Computer Science, 107:3-30, 1993. Google Scholar
  3. Rahul Arora, Ashu Gupta, Rohit Gurjar, and Raghunath Tewari. Derandomizing isolation lemma for k_3, 3-free and k₅-free bipartite graphs. In 33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016, February 17-20, 2016, Orléans, France, pages 10:1-10:15, 2016. Google Scholar
  4. Greg Barnes, Jonathan F. Buss, Walter L. Ruzzo, and Baruch Schieber. A sublinear space, polynomial time algorithm for directed s-t connectivity. In Structure in Complexity Theory Conference, 1992., Proceedings of the Seventh Annual, pages 27-33, 1992. Google Scholar
  5. David A. Mix Barrington. Bounded-width polynomial-size branching programs recognize exactly those languages in NC¹. Journal of Computer and System Sciences, 38:150-164, 1989. Google Scholar
  6. David A. Mix Barrington, Chi-Jen Lu, Peter Bro Miltersen, and Sven Skyum. Searching constant width mazes captures the ∿⁰ hierarchy. In 15th International Symposium on Theoretical Aspects of Computer Science (STACS), Volume 1373 in Lecture Notes in Computer Science, pages 74-83. Springer, 1998. Google Scholar
  7. Chris Bourke, Raghunath Tewari, and N. V. Vinodchandran. Directed planar reachability is in unambiguous log-space. In 22nd Annual IEEE Conference on Computational Complexity (CCC 2007), 13-16 June 2007, San Diego, California, USA, pages 217-221, 2007. URL: http://dx.doi.org/10.1109/CCC.2007.9.
  8. Gerhard Buntrock, Birgit Jenner, Klaus-Jörn Lange, and Peter Rossmanith. Unambiguity and fewness for logarithmic space. In Proceedings of the 8th International Conference on Fundamentals of Computation Theory (FCT'91), Volume 529 Lecture Notes in Computer Science, pages 168-179. Springer-Verlag, 1991. Google Scholar
  9. Diptarka Chakraborty, Aduri Pavan, Raghunath Tewari, N. V. Vinodchandran, and Lin F. Yang. New time-space upperbounds for directed reachability in high-genus and h-minor-free graphs. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science, FSTTCS 2014, December 15-17, 2014, New Delhi, India, pages 585-595, 2014. Google Scholar
  10. Diptarka Chakraborty and Raghunath Tewari. An O(n^ε) space and polynomial time algorithm for reachability in directed layered planar graphs. In In 26th International Symposium on Algorithms and Computation, ISAAC 2015, Nagoya, Japan, December 9-11, 2015, pages 614-624, 2015. Google Scholar
  11. Samir Datta, Raghav Kulkarni, Raghunath Tewari, and N. V. Vinodchandran. Space Complexity of Perfect Matching in Bounded Genus Bipartite Graphs. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011), volume 9 of Leibniz International Proceedings in Informatics (LIPIcs), pages 579-590, Dagstuhl, Germany, 2011. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik. URL: http://dx.doi.org/10.4230/LIPIcs.STACS.2011.579.
  12. Kousha Etessami. Counting quantifiers, successor relations, and logarithmic space. Journal of Computer and System Sciences, 54(3):400-411, June 1997. Google Scholar
  13. Stephen A. Fenner, Rohit Gurjar, and Thomas Thierauf. Bipartite perfect matching is in quasi-nc. CoRR, abs/1601.06319, 2016. URL: http://arxiv.org/abs/1601.06319.
  14. Michael L. Fredman, János Komlós, and Endre Szemerédi. Storing a sparse table with 0(1) worst case access time. J. ACM, 31(3):538-544, June 1984. URL: http://dx.doi.org/10.1145/828.1884.
  15. Anna Gál and Avi Wigderson. Boolean complexity classes vs. their arithmetic analogs. Random Struct. Algorithms, 9(1-2):99-111, 1996. URL: http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1098-2418(199608/09)9:1/2<99::AID-RSA7>3.0.CO;2-6/abstract.
  16. T. Imai, K. Nakagawa, A. Pavan, N.V. Vinodchandran, and O. Watanabe. An O(n^1/2+ε)-Space and Polynomial-Time Algorithm for Directed Planar Reachability. In Computational Complexity (CCC), 2013 IEEE Conference on, pages 277-286, 2013. URL: http://dx.doi.org/10.1109/CCC.2013.35.
  17. Neil Immerman. Nondeterministic space is closed under complement. SIAM Journal on Computing, 17:935-938, 1988. Google Scholar
  18. Jan Kynčl and Tomáš Vyskočil. Logspace reduction of directed reachability for bounded genus graphs to the planar case. ACM Transactions on Computation Theory, 1(3):1-11, 2010. URL: http://dx.doi.org/10.1145/1714450.1714451.
  19. Aduri Pavan, Raghunath Tewari, and N. V. Vinodchandran. On the power of unambiguity in log-space. Computational Complexity, 21(4):643-670, 2012. URL: http://dx.doi.org/10.1007/s00037-012-0047-3.
  20. Omer Reingold. Undirected connectivity in log-space. Journal of the ACM, 55(4), 2008. Google Scholar
  21. Klaus Reinhardt and Eric Allender. Making nondeterminism unambiguous. SIAM J. Comput., 29(4):1118-1131, 2000. URL: http://dx.doi.org/10.1137/S0097539798339041.
  22. Walter J. Savitch. Relationships between nondeterministic and deterministic tape complexities. J. Comput. Syst. Sci., 4:177-192, 1970. Google Scholar
  23. Robert Szelepcsényi. The method of forced enumeration for nondeterministic automata. Acta Informatica, 26:279-284, 1988. Google Scholar
  24. Thomas Thierauf and Fabian Wagner. Reachability in K_3,3-free Graphs and K₅-free Graphs is in Unambiguous Log-Space. In 17th International Conference on Foundations of Computation Theory (FCT), Lecture Notes in Computer Science 5699, pages 323-334. Springer-Verlag, 2009. Google Scholar
  25. Leslie G. Valiant. Relative complexity of checking and evaluating. Inf. Process. Lett., 5(1):20-23, 1976. URL: http://dx.doi.org/10.1016/0020-0190(76)90097-1.
  26. Avi Wigderson. The complexity of graph connectivity. Mathematical Foundations of Computer Science 1992, pages 112-132, 1992. Google Scholar
  27. Avi Wigderson. NL/poly ⊆ ⊕ L/poly (preliminary version). In Proceedings of the Ninth Annual Structure in Complexity Theory Conference, Amsterdam, The Netherlands, June 28 - July 1, 1994, pages 59-62, 1994. URL: http://dx.doi.org/10.1109/SCT.1994.315817.
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
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact