Acta Informatica

, Volume 30, Issue 3, pp 267–278 | Cite as

Relations among simultaneous complexity classes of nondeterministic and alternating Turing machines

  • Shigeki Iwata
  • Takumi Kasai
  • Etsuro Moriya


Ruzzo [Tree-size bounded alternation, J. Comput. Syst. Sci. 21] introduced the notion of tree-size for alternating Turing machines (ATMs) and showed that it is a reasonable measure for classification of complexity classes. We establish in this paper that computations by tree-size and space simultaneously bounded ATMs roughly correspond to computations by time and space simultaneously bounded nondeterministic TMs (NTMs).

We also show that not every polynomial time bounded and sublinear space simultaneously bounded NTM can be simulated by any deterministic TM with a slightly increased time bound and a slightly decreased space bound simultaneously.


Information System Operating System Data Structure Communication Network Information Theory 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bruss, A.R., Meyer, A.R.: On time-space classes and their relation to the theory of addition. Theor. Comput. Sci.11, 59–69 (1980)Google Scholar
  2. [2]
    Fischer, M.J., Rosenberg, A.L.: Real-time solutions of the origin-crossing problem. Math. Syst. Theory2, 257–263 (1968)Google Scholar
  3. [3]
    Hopcroft, J.E., Ullman, J.D.: Introduction to automata theory, languages, and computation. Reading, MA: Addison-Wesley 1979Google Scholar
  4. [4]
    Kannan, R.: Alternation and the power of nondeterminism. Proceedings 15th Annual ACM Symposium on Theor. of Comput., pp. 344–346 (1983)Google Scholar
  5. [5]
    Kannan, R.: Towards separating nondeterminism from determinism. Math. Syst. Theory17, 29–45 (1984)Google Scholar
  6. [6]
    Monien, B., Sudborough, I.H.: Bandwidth constrained NP-complete problems. Theor. Comput. Sci.41, 141–168 (1985)Google Scholar
  7. [7]
    Moriya, E., Iwata, S., Kasai, T.: A note on some simultaneous relations among time, space, and reversal for single worktape offline Turing machines. Inf. Contr.70, 179–185 (1986)Google Scholar
  8. [8]
    Paul, W.J., Pippenger, N., Szemerédi, E., Trotter, W.T.: On determinism versus nondeterminism and related problems. Proceedings 24th Annual Symposium on Foundation of Computer Science, pp. 429–438 (1983)Google Scholar
  9. [9]
    Pippenger, N., Fischer, M.: Relations among complexity measures. J. Assoc. Comput. Mach.26, 361–381 (1979)Google Scholar
  10. [10]
    Ruzzo, W.L.: Tree-size bounded alternation. J. Comput. Syst. Sci.21, 218–235 (1980)Google Scholar
  11. [11]
    Ruzzo, W.L.: On uniform circuit complexity. J. Comput. Syst. Sci.22, 365–383 (1981)Google Scholar
  12. [12]
    Seiferas, J.I., Fischer, M.J., Meyer, A.R.: Separating nondeterministic time complexity classes. J. Assoc. Comput. Mach.25, 146–167 (1978)Google Scholar
  13. [13]
    Sudborough, I.H.: A note on tape bounded complexity classes and linear context-free languages. J. Assoc. Comput. Mach.22, 499–500 (1975)Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Shigeki Iwata
    • 1
  • Takumi Kasai
    • 2
  • Etsuro Moriya
    • 3
  1. 1.Information Science LaboratoryTokai UniversityHiratsuka, KanagawaJapan
  2. 2.Department of Computer ScienceUniversity of Electro-CommunicationsChofuJapan
  3. 3.Department of MathematicsTokyo Woman's Christian UniversityTokyoJapan

Personalised recommendations