Skip to main content
SpringerLink
Log in
Book cover

International Colloquium on Automata, Languages, and Programming

ICALP 1995: Automata, Languages and Programming pp 183–195Cite as

Lower time bounds for randomized computation

  • Computational Complexity I
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 944))

Abstract

It is a fundamental problem in the randomized computation how to separate different randomized time or randomized space classes (c.f., e.g., [KV87, KV88]). We have separated randomized space classes below log n in [FK94]. Now we have succeeded to separate small randomized time classes for multi-tape 2-way Turing machines. Surprisingly, these “small” bounds are of type n+f(n) with f(n) not exceeding linear functions. This new approach to “sublinear” time complexity is a natural counterpart to sublinear space complexity. The latter was introduced by considering the input tape and the work tape as separate devices and distinguishing between the space used for processing information and the space used merely to read the input word from. Likewise, we distinguish between the time used for processing information and the time used merely to read the input word.

Research partially supported by Grant No.93-599 from the Latvian Council of Science

Research partially supported by the International Computer Science Institute, Berkeley, California, by the DFG grant KA 673/4-1, and by the ESPRIT BR Grants 7079 and ECUS030

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Freivalds, R., Fast computations by probabilistic Turing machines, Proceedings of Latvian State University, 233(1975), pp. 201–205 (Russian)

    Google Scholar 

  2. Freivalds, R., Probabilistic machines can use Isess runnning time, Information Processing'77 (Proc. IFIP Congress'77), North Holland, 1977, pp. 839–842

    Google Scholar 

  3. Freivalds, R., Speeding up recognition of some sets by usage of random number generators, Problemi kibernetiki, 36(1979), pp. 209–224 (Russian)

    Google Scholar 

  4. Freivalds, R., Probabilistic two-way machines, LNCS, 118(1981), pp.33–45

    Google Scholar 

  5. Freivalds, R., Space and reversal complexity of probabilistic one-way Turing machines, LNCS, 158(1983), pp. 159–170

    Google Scholar 

  6. Freivalds, R., Space and reversal complexity of probabilistic one-way Turing machines, Annals of Discrete Mathematics, 24(1985), pp. 39–50

    Google Scholar 

  7. Freivalds, R., Ikaunieks, E., On advantages of nondeterministic machines over probabilistic ones, Izvestiya VUZ. Matematika, No.2(177), 1977, pp.108–123 (Russian)

    Google Scholar 

  8. Freivalds, R., Karpinski, M., Lower space bounds for randomized computation, Lecture Notes in Computer Science, vol. 820(1994), pp. 580–592

    Google Scholar 

  9. Gallager, R.G., Information Theory and Reliable Communication. John Wiley, NY, 1968

    Google Scholar 

  10. Ja'Ja', J., Prasanna Kumar, V.K., Simon, J., Information transfer under different sets of protocols, SIAM J. Computation, 13(1984), pp.840–849

    Google Scholar 

  11. Kaneps, J. and Freivalds R., Minimal nontrivial space complexity of probabilistic one-way Turing machines, LNCS, 452(1990), pp. 355–361

    Google Scholar 

  12. Karpinski, M. and Verbeek, R., On the Monte Carlo space constructible functions and space separation results for probabilistic complexity classes, Information and Computation, 75(1987), pp. 178–189

    Google Scholar 

  13. Karpinski, M. and Verbeek, R., Randomness, probability, and the separation of Monte Carlo time and space, LNCS, 270(1988), pp. 189–207

    Google Scholar 

  14. Karpinski, M. and Verbeek, R., On randomized versus deterministic computation, Proc. ICALP'93, LNCS, 700(1993), pp. 227–240

    Google Scholar 

  15. Ming Li, Paul Vitanyi, An Introduction to Kolmogorov Complexity and Its Applications, Springer, 1993

    Google Scholar 

  16. Stearns, R.E., Hartmanis, J., Lewis, P.M., Hiearchies of memory limited computations, Proc. IEEE Conference on Switch., Circuit Theory and Logical Design, 1965, pp. 179–190

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, University of Latvia, Raina bulv. 29, Riga, Latvia

    RŪsiņš Freivalds

  2. Department of Computer Science, University of Bonn, 53117, Bonn, Germany

    Marek Karpinski

Authors
  1. RŪsiņš Freivalds
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marek Karpinski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Zoltán Fülöp Ferenc Gécseg

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Freivalds, R., Karpinski, M. (1995). Lower time bounds for randomized computation. In: Fülöp, Z., Gécseg, F. (eds) Automata, Languages and Programming. ICALP 1995. Lecture Notes in Computer Science, vol 944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60084-1_73

Download citation

  • DOI: https://doi.org/10.1007/3-540-60084-1_73

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60084-8

  • Online ISBN: 978-3-540-49425-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation