A Time Hierarchy Theorem for Nondeterministic Cellular Automata

  • Chuzo Iwamoto
  • Harumasa Yoneda
  • Kenichi Morita
  • Katsunobu Imai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4484)


We present a tight time-hierarchy theorem for nondeterministic cellular automata by using a recursive padding argument. It is shown that, if t 2(n) is a time-constructible function and t 2(n) grows faster than t 1(n + 1), then there exists a language which can be accepted by a t 2(n)-time nondeterministic cellular automaton but not by any t 1(n)-time nondeterministic cellular automaton.


Cellular Automaton Cellular Automaton Input String Encode Sequence Random Access Machine 
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  1. 1.
    Cook, S.A.: A hierarchy for nondeterministic time complexity. J. Comput. System Sci. 7, 343–353 (1973)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Cook, S.A., Reckhow, R.A.: Time bounded random access machines. J. Comput. System Sci. 7, 354–375 (1973)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Fürer, M.: The tight deterministic time hierarchy. In: Proc. ACM Symp. on Theory of Computing, pp. 8–16 (1982)Google Scholar
  4. 4.
    Hartmanis, J., Stearns, R.E.: On the computational complexity of algorithms. Trans. Amer. Math. Soc. 117, 285–306 (1965)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Hennie, F.C.: One-tape off-line Turing machine computations. Inform. Contr. 8, 553–578 (1965)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Ibarra, O.H.: A note concerning nondeterministic tape complexity. J. Assoc. Comput. Mach. 19, 608–612 (1972)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Iwama, K., Iwamoto, C.: Parallel complexity hierarchies based on PRAMs and DLOGTIME-uniform circuits. In: Proc. 11th IEEE Conf. on Computational Complexity, pp. 24–32 (1996)Google Scholar
  8. 8.
    Iwama, K., Iwamoto, C.: Improved time and space hierarchies of one-tape off-line TMs. In: Brim, L., Gruska, J., Zlatuška, J. (eds.) MFCS 1998. LNCS, vol. 1450, pp. 580–588. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  9. 9.
    Iwamoto, C., et al.: Computational complexity in the hyperbolic plane. In: Diks, K., Rytter, W. (eds.) MFCS 2002. LNCS, vol. 2420, pp. 365–374. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Iwamoto, C., et al.: Hierarchies of DLOGTIME-uniform circuits. In: Margenstern, M. (ed.) MCU 2004. LNCS, vol. 3354, pp. 211–222. Springer, Heidelberg (2005)Google Scholar
  11. 11.
    Iwamoto, C., et al.: Constructible functions in cellular automata and their applications to hierarchy results. Theoret. Comput. Sci. 270, 797–809 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Iwamoto, C., Margenstern, M.: Time and space complexity classes of hyperbolic cellular automata. IEICE Trans. on Information and Systems E87-D(3), 700–707 (2004)Google Scholar
  13. 13.
    Iwamoto, C., et al.: Translational lemmas for alternating TMs and PRAMs. In: Liśkiewicz, M., Reischuk, R. (eds.) FCT 2005. LNCS, vol. 3623, pp. 126–137. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Loryś, K.: New time hierarchy results for deterministic TMs. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol. 577, pp. 329–336. Springer, Heidelberg (1992)Google Scholar
  15. 15.
    Mazoyer, J.: A 6-state minimal time solution to the firing squad synchronization problem. Theoret. Comput. Sci. 50, 183–238 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Paul, W.J.: On time hierarchies. J. Comput. System Sci. 19, 197–202 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Paul, W.J., Prauß, E.J., Reischuk, R.: On alternation. Acta Inform. 14, 243–255 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Rogers Jr., H.: Theory of recursive functions and effective computability. McGraw-Hill, New York (1967)zbMATHGoogle Scholar
  19. 19.
    Seiferas, J.I.: Nondeterministic time and space complexity classes. MIT-LCS-TR-137, Proj. MAC, MIT, Cambridge, Mass. (Sept. 1974)Google Scholar
  20. 20.
    Seiferas, J.I., Fischer, M.J., Meyer, A.R.: Separating nondeterministic time complexity classes. J. Assoc. Comput. Mach. 25(1), 146–167 (1978)zbMATHMathSciNetGoogle Scholar
  21. 21.
    Sipser, M.: Introduction to the theory of computation. PWS Publishing, Boston (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Chuzo Iwamoto
    • 1
  • Harumasa Yoneda
    • 1
  • Kenichi Morita
    • 1
  • Katsunobu Imai
    • 1
  1. 1.Hiroshima University, Graduate School of Engineering, Higashi-Hiroshima, 739-8527Japan

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