On the computing power of one-way cellular arrays

  • Oscar H. Ibarra
  • Tao Jiang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 267)


There are two simple models of parallel language recognizer: one-way cellular array (OCA) and one-way iterative array (OIA). For inputs of length n, both arrays consist of n identical finite-state machines (cells). The communication between cells is one-way, from left to right. The difference in the two models is in the manner in which the input is applied. For the OCA, the input is applied to the cells in parallel. For the OIA, the input is applied serially to the leftmost processor. An input string is accepted if the rightmost cell eventually enters an accepting state. We show that OCA's accept exactly the same class of languages as OIA's. It is relatively easy to show that OIA's can simulate OCA's. The difficult part is the converse, i.e., that OCA's can simulate OIA's. This is rather surprising since in an OIA, every cell of the array has access to each symbol of the input string, whereas in an OCA, the i-th cell can only access the first i symbols of the input. This result when combined with known results concerning OIA's answers some open questions concerning the computational complexity of OCA's. We also prove some new results concerning linear-time OCA's and OIA's. For example, we show: (1) linear-time OCA's are equivalent to 2n-time OIA's (note that 2n-time is optimal for OIA's); (2) the concatenation of a linear-time OCA language with a real-time (i.e., n-time) OCA language is a linear-time OCA language; (3) every semilinear language is a linear-time OCA language.


Cellular Automaton Input Pattern Sequential Machine Input String Input Symbol 
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. [CHAN81]
    Chandra, A., D. Kozen and L. Stockmeyer, Alternation, J. ACM 28-1, 1981, pp. 114–133.Google Scholar
  2. [CHAN83]
    Chan, T. and O. Ibarra, On the space and time complexity of functions computable by simple programs, SICOMP 12-4, 1983, pp. 708–716.Google Scholar
  3. [CHAN86a]
    Chang, J., O. Ibarra and M. Palis, Efficient simulations of simple models of parallel computation by space-bounded TMs and time-bounded alternating TMs, Revision of Tech. Rep. 85-47, Department of Computer Science, University of Minnesota, Nov. 1985; submitted to Theoretical Computer Science.Google Scholar
  4. [CHAN86b]
    Chang, J., O. Ibarra and A. Vergis, On the power of one-way communication, Proceedings of the 27th IEEE Annual Symposium on Foundations of Computer Science, 1986, pp. 455–464.Google Scholar
  5. [CHOF84]
    Choffrut, C. and K. Culik II, On real-time cellular automata and trellis automata, Acta Inform. 21, 1984, pp. 393–409.CrossRefGoogle Scholar
  6. [COOK71]
    Cook, S., Characterizations of pushdown machines in terms of time-bounded computers, J. ACM 18-1, 1971, pp. 4–18.CrossRefGoogle Scholar
  7. [CULI84]
    Culik II, K., J. Gruska and A. Salomaa, Systolic trellis aotumata; Part I, Internat. J. Comput. Math. 15, 1984, pp. 195–212.Google Scholar
  8. [DYER80]
    Dyer, C., One-way bounded cellular automata, Information and Control 44, 1980, pp. 54–69.CrossRefGoogle Scholar
  9. [GURA79]
    Gurari, E. and O. Ibarra, The complexity of the equivalence problem for two characterizations of Presburger sets, Theoretical Computer Science 13, pp. 295–314.Google Scholar
  10. [HARR68]
    Harrison, M. and O. Ibarra, Multitape and Multihead pushdown automata, Information and Control 13, 1968, pp. 433–470.CrossRefGoogle Scholar
  11. [HARR78]
    Harrison, M., Introduction to formal language theory, Addison-Wesley, 1978.Google Scholar
  12. [HENN61]
    Hennie, F., Iterative arrays of logical circuits, MIT Press, Cambridge, Mass., 1961.Google Scholar
  13. [HOPC79]
    Hopcroft, J. and J. Ullman, Introduction to automata theory, languages, and computation, Addison-Wesley, 1979.Google Scholar
  14. [IBAR74]
    Ibarra, O., A note on semilinear sets and bounded-reversal multihead pushdown automata, Inform. Process. lett. 3, 1974, pp. 25–28.CrossRefGoogle Scholar
  15. [IBAR85a]
    Ibarra O., and M. Palis, Two-dimensional systolic arrays: characterizations and applications, Tech. Rep. 85-1, Department of Computer Science, University of Minnesota, Jan. 1985; to appear in Theoretical Computer Science.Google Scholar
  16. [IBAR85b]
    Ibarra, O., M. Palis and S. Kim, Some results concerning linear iterative (systolic) arrays, J. of Parallel and Distributed Computing 2, 1985, pp. 182–218.CrossRefGoogle Scholar
  17. [IBAR86]
    Ibarra, O., S. Kim and M. Palis, Designing Systolic Algorithms using sequential machines, IEEE Trans. on Computers C35-6, June 1986, pp. 31–42; extended abstract in Proc. 25th IEEE Symposium on Foundations of Computer Science, 1984, pp. 46–55.Google Scholar
  18. [SEID79]
    Seidel, S., Language recognition and the synchronization of cellular automata, Tech. Rep. 79-02, Department of Computer Science, University of Iowa, 1979.Google Scholar
  19. [SMIT70]
    Smith, A., III, Cellular automata and formal languages, Proc. 11th IEEE Ann. Symp. on Switching and Automata Theory, 1970, pp. 216–224.Google Scholar
  20. [SMIT71]
    Smith, A., III, Cellular automata complexity trade-offs, Information and Control 18, 1971, pp. 466–482.CrossRefGoogle Scholar
  21. [UMEO82]
    Umeo, H., K. Morita, and K. Sugata, Deterministic one-way simulation of two-way real-time cellular automata and its related problems, Inform. Process. Lett. 14, 1982, pp. 159–161.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Oscar H. Ibarra
    • 1
  • Tao Jiang
    • 1
  1. 1.Department of Computer ScienceUniversity of MinnesotaMinneapolis

Personalised recommendations