Iterative Arrays with Small Time Bounds

  • Thomas Buchholz
  • Andreas Klein
  • Martin Kutrib
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1893)


An iterative array is a line of interconnected interacting finite automata. One distinguished automaton, the communication cell, is connected to the outside world and fetches the input serially symbol by symbol. Sometimes in the literature this model is referred to as cellular automaton with sequential input mode. We investigate deterministic iterative arrays (IA) with small time bounds between real-time and linear-time. It is shown that there exists an infinite dense hierarchy of strictly included complexity classes in that range. The result closes the last gap in the time hierarchy of IAs.


Iterative arrays cellular automata computational complexity time hierarchies 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Beyer, W. T. Recognition of topological invariants by iterative arrays. Technical Report TR-66, MIT, Cambridge, Proj. MAC, 1969.Google Scholar
  2. 2.
    Buchholz, Th. and Kutrib, M. On the power of one-way bounded cellular time computers. Developments in Language Theory, 1997, pp. 365–375.Google Scholar
  3. 3.
    Buchholz, Th. and Kutrib, M. Some relations between massively parallel arrays. Parallel Comput. 23 (1997), 1643–1662.CrossRefMathSciNetGoogle Scholar
  4. 4.
    Buchholz, Th. and Kutrib, M. On time computability of functions in one-way cellular automata. Acta Inf. 35 (1998), 329–352.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Buchholz, Th., Klein, A., and Kutrib, M. Deterministic turing machines in the range between real-time and linear-time. To appear.Google Scholar
  6. 6.
    Chang, J. H., Ibarra, O. H., and Palis, M. A. Parallel parsing on a one-way array of finite-state machines. IEEE Trans. Comput. C-36 (1987), 64–75.CrossRefGoogle Scholar
  7. 7.
    Cole, S. N. Real-time computation by n-dimensional iterative arrays of finite-state machines. IEEE Trans. Comput. C-18 (1969), 349–365.MathSciNetCrossRefGoogle Scholar
  8. 8.
    Čulik II, K. and Yu, S. Iterative tree automata. Theoret. Comput. Sci. 32 (1984), 227–247.CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Fischer, P. C. Generation of primes by a one-dimensional real-time iterative array. J. Assoc. Comput. Mach. 12 (1965), 388–394.Google Scholar
  10. 10.
    Ibarra, O. H. and Jiang, T. On one-way cellular arrays. SIAM J. Comput. 16 (1987), 1135–1154.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Ibarra, O. H. and Palis, M. A. Some results concerning linear iterative (systolic) arrays. J. Parallel and Distributed Comput. 2 (1985), 182–218.CrossRefGoogle Scholar
  12. 12.
    Ibarra, O. H. and Palis, M. A. Two-dimensional iterative arrays: Characterizations and applications. Theoret. Comput. Sci. 57 (1988), 47–86.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Iwamoto, C., Hatsuyama, T., Morita, K., and Imai, K. On time-constructible functions in one-dimensional cellular automata. Fundamentals of Computation Theory 1999, LNCS 1684, 1999, pp. 317–326.CrossRefGoogle Scholar
  14. 14.
    Mazoyer, J. and Terrier, V. Signals in one dimensional cellular automata. Theoret. Comput. Sci. 217 (1999), 53–80.zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Seiferas, J. I. Iterative arrays with direct central control. Acta Inf. 8 (1977), 177–192.zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Seiferas, J. I. Linear-time computation by nondeterministic multidimensional iterative arrays. SIAM J. Comput. 6 (1977), 487–504.zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Smith III, A. R. Real-time language recognition by one-dimensional cellular automata. J. Comput. System Sci. 6 (1972), 233–253.zbMATHMathSciNetGoogle Scholar
  18. 18.
    Terrier, V. On real time one-way cellular array. Theoret. Comput. Sci. 141 (1995), 331–335.zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Wagner, K. and Wechsung, G. Computational Complexity. Reidel Publishing, Dordrecht, 1986.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Thomas Buchholz
    • 1
  • Andreas Klein
    • 1
  • Martin Kutrib
    • 1
  1. 1.Institute of InformaticsUniversity of GiessenGiessenGermany

Personalised recommendations