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New time hierarchy results for deterministic TMS

  • Krzysztof Loryś
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 577)

Abstract

We show a method of maintaining a distributed counter by 2-dimensional deterministic Turing machines with at least two tapes. Our method yields a tight time hierarchy for these machines solving an open problem posed by M. Fürer ([Fü1],[Fü2]). Moreover, we improve the best known time hierarchy theorem for one-tape off-line deterministic TMs; among others we show that this hierarchy is tight for functions bounded by polynomials.

Keywords

Turing Machine Simulated Step Input Word Input Tape Universal Machine 
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. [Fü1]
    M. Fürer. The tight deterministic time hierarchy. 14th STOC (1982), 8–16.Google Scholar
  2. [Fü2]
    M. Fürer. Data structures for distributed counting. JCSS 28 (1984), 231–243.Google Scholar
  3. [Ha]
    J. Hartmanis. Computational complexity of one-tape Turing machine computations. JACM 15 (1968), 325–339.Google Scholar
  4. [He]
    F.C. Hennie. One-tape off-line Turing machine computations. Inform. and Contr. 8 (1965), 553–578.Google Scholar
  5. [HeSt]
    F.C. Hennie and R.E. Stearns. Two-tape simulation of multitape Turing machines JACM 13 (1966), 533–546.Google Scholar
  6. [MaScSz]
    W. Maass, G. Schnitger and E. Szemeredi. Two tapes are better than one for off-line Turing machines. 19th STOC (1987), 94–100.Google Scholar
  7. [Pa]
    W.J. Paul. On time hierarchies. 9th STOC (1977), 218–222.Google Scholar
  8. [PaPrRe]
    W.J. Paul, E.J. Preuß and R. Reischuk. On alternation. Acta Informatica 14 (1980), 243–255.Google Scholar
  9. [RuFi]
    S.S. Ruby and P.C. Fischer. Translational methods and computational complexity. 6th Ann. Symp. on Circiut Theory and Log. Design (1965), 173–178.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Krzysztof Loryś
    • 1
  1. 1.Institute of Computer ScienceUniversity of WroclawWroclawPoland

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