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Nearly linear time

  • Yuri Gurevich
  • Saharon Shelah
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 363)

Abstract

The notion of linear-time computability is very sensitive to machine model. In this connection, we introduce a class NLT of functions computable in nearly linear time n(log n)O(1) on random access computers. NLT is very robust and does not depend on the particular choice of random access computers. Kolmogorov machines, Schönhage machines, random access Turing machines, etc., also compute exactly NLT functions in nearly linear time. It is not known whether usual multitape Turing machines are able to compute all NLT functions in nearly linear time. We do not believe they are and do not consider them necessarily appropriate for this relatively low complexity level. It turns out, however, that nondeterministic Turing machines accept exactly the languages in the nondeterministic version of NLT. We give also a machine-independent definition of NLT and a natural problem complete for NLT.

Keywords

Linear Time Turing Machine Binary String Machine Model Parameter String 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    G. M. Adelson-Velsky. Soviet Math. 3 (1962), 1259–1263.Google Scholar
  2. [2]
    A. V. Aho, J. E. Hopcroft and J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Mass. 1974.Google Scholar
  3. [3]
    Dana Angluin and Les Valiant. Fast Probabilistic Algorithm for Hamiltonian Circuits and Matchings. J. of Computer and System Sciences 18 (1979), 155–193.Google Scholar
  4. [4]
    Stephen A. Cook. Short Propositional Formulas Represent Nondeterministic Computations. IPL 26 (1987/88), 269–270.Google Scholar
  5. [5]
    Yuri Gurevich. Kolmogorov Machines and Related Issues: The Column on Logic in Computer Science. Bulletin of European Assoc. for Theor. Comp. Science 35, June 1988, 71–82.Google Scholar
  6. [6]
    Yuri Gurevich and Saharon Shelah. Functions Computable in Nearly Linear Time. AMS Abstracts 7:4 (1986), p. 236.Google Scholar
  7. [7]
    Donald E. Knuth. The Art of Computer Programming: Volume 3 / Sorting and Searching. Addison-Wesley, Reading, Mass. 1973.Google Scholar
  8. [8]
    A. N. Kolmogorov and V. A. Uspensky. On the Definition of an Algorithm. Uspekhi Mat. Nauk 13:4 (1958), 3–28 (Russian) or AMS Translations, ser. 2, vol. 21 (1963), 217–245.Google Scholar
  9. [9]
    Sandy Irani, Moni Naor, Ronitt Rubinfeld. On the Time and Space Complexity of Computation Using Write-Once Memory. Manuscript, Computer Science Division, UC Berkeley, Nov. 1988.Google Scholar
  10. [10]
    W. J. Paul, N. Pippenger, E. Szemeredi and W. T. Trotter, On determinism versus non-determinism and related problems. Proc. 24th IEEE Symposium on Foundation of Computer Science, November 1983, Tucson, Arizona, 429–438.Google Scholar
  11. [11]
    N. Pippinger and M. J. Fischer. Relations among Complexity Measures. J. ACM 26:2 (1979), 361–381.Google Scholar
  12. [12]
    Claus P. Schnorr. Satisfiability is Quasilinear Complete in NQL. Journal of ACM 25:1 (1978), 136–145.Google Scholar
  13. [13]
    A. Schönhage. Storage Modification Machines. SIAM J. Computing 9:3, August 1980, 490–508.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Yuri Gurevich
    • 1
  • Saharon Shelah
    • 2
    • 3
  1. 1.Electrical Engineering and Computer ScienceUniversity of MichiganAnn Arbor
  2. 2.MathematicsHebrew UniversityJerusalemIsrael
  3. 3.MathematicsRutgers UniversityNew Brunswick

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