Advertisement

On some open problems concerning the complexity of cellular arrays

  • Oscar H. Ibarra
  • Tao Jiang
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 812)

Abstract

We give a brief account of the progress that has been made in the last few years concerning the computational complexity of cellular arrays, and cite a few important open problems that remain unresolved.

Key words

Cellular array computational complexity one-way communication mesh-connected tree-connected 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BUCH84]
    Bucher, W. and K. Culik II, On real time and linear time cellular automata, R.A.I.R.O. Informatique theorique/Theoretical Infomatics 18-4, 1984, pp. 307–325.Google Scholar
  2. [CHAN81b]
    Chandra, A., D. Kozen and L. Stockmeyer, Alternation, J. ACM 28-1, 1981, pp. 114–133.Google Scholar
  3. [CHAN88a]
    Chang, J., O. Ibarra, and M. Palis, Efficient simulations of simple models of parallel computation by space-bounded TMs and time-bounded alternating TMs, in the Proceedings of the 14th ICALP, 1988, Finland; expanded version in Theoretical Computer Science 68, 19–36, 1989.Google Scholar
  4. [CHAN88b]
    Chang, J., O. Ibarra, and A. Vergis, On the power of one-way communication, J. ACM 35, 1988, pp. 697–726.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.Google Scholar
  6. [COLE69]
    Cole, S., Real-time computation by n-dimensional iterative arrays of finite-state machines, IEEE Trans. Comput. 18-4, 1969, pp. 346–365.Google Scholar
  7. [CULI84]
    Culik II, K., J. Gruska, and A. Salomaa, Systolic trellis automata: Part I, Internat. J. Comput. Math. 15, 1984, pp. 195–212.Google Scholar
  8. [CULI86]
    Culik II, K., O. Ibarra, and S. Yu, Iterative Tree Arrays with Logarithmic Depth, Intern. J. Computer Math. 20, 1986, pp. 187–204.Google Scholar
  9. [DYER80]
    Dyer, C., One-way bounded cellular automata, Information and Control 44, 1980, pp. 54–69.Google Scholar
  10. [DYER81]
    Dyer, C. and Rosenfeld, A., Triangle Cellular Automata, Information and Control 48, 1981, pp. 54–69.Google 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. [IBAR84]
    Ibarra, O. and S. Kim, Characterizations and computational complexity of systolic trellis automata, Theor. Comput. Sci. 29, 1984, pp. 123–153.Google Scholar
  15. [IBAR85a]
    Ibarra, O., S. Kim, and S. Moran, Sequential machine characterizations of trellis and cellular automata and applications, SIAM J. Computing 14, 1985, pp. 426–447.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.Google Scholar
  17. [IBAR86]
    Ibarra, O., S. Kim, and M. Palis, Designing Systolic Algorithms using sequential machines, IEEE Trans. on Computers C35-6, 1986, pp. 31–42; extended abstract in Proc. 25th IEEE Symposium on Foundations of Computer Science, 1984, pp. 46–55.Google Scholar
  18. [IBAR87]
    Ibarra, O. and Jiang, T., On one-way cellular arrays, SIAM J. on Computing 16, 1987, pp. 1135–1154; prelim. version in Proc. 13th ICALP, 1987, Karlsruhe, West Germany.Google Scholar
  19. [IBAR88a]
    Ibarra, O., and M. Palis, Two-dimensional systolic arrays: characterizations and applications, Theoretical Computer Science 57, 1988, pp. 47–86.Google Scholar
  20. [IBAR88b]
    Ibarra, O. and T. Jiang, Relating the power of cellular arrays to their closure properties, Theoretical Computer Science 57, 1988, 225–238.Google Scholar
  21. [IBAR89a]
    O. Ibarra, T. Jiang, and J. Chang, On iterative and cellular tree arrays, Journal of Computer and System Sciences 38, 1989, pp. 452–473.Google Scholar
  22. [IBAR89b]
    Ibarra, O. and T. Jiang, Optimal simulation of tree arrays by linear arrays, Inform. Process. Lett. 30, 1989, pp. 295–302.Google Scholar
  23. [KOSA74]
    Kosaraju, S., On some open problems in the theory of cellular automata, IEEE Trans. on Computers C-23, 1974, pp. 561–565.Google Scholar
  24. [PATE72]
    Paterson, M., Tape bounds for time-bounded Turing machines, J. Comp. System Sci. 6, 1972, pp. 116–124.Google Scholar
  25. [PATE81]
    Paterson, M., W. Ruzzo, and L. Snyder, Bounds on minmax edge length for complete binary trees, Proc. 13th ACM Symposium on the Theory of Computing, 1981, pp. 293–299.Google Scholar
  26. [SAVI70]
    Savitch, W., Relationships between nondeterministic and deterministic complexities, J. Comp. System Sci. 4, 1970, pp. 177–192.Google Scholar
  27. [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
  28. [SMIT71]
    Smith, A., III, Cellular automata complexity trade-offs, Information and Control 18, 1971, pp. 466–482.Google Scholar
  29. [SMIT72]
    Smith, A., III, Real-time language recognition by one-dimensional cellular automata, J. Comp. System Sci. 6, 1972, pp. 233–253.Google Scholar
  30. [UMEO82]
    Umeo, H., K. Morita, and K. Sugata, Deterministic one-way simulation of two-way realtime cellular automata and its related problems, Inform. Process. Lett. 14, 1982, pp. 159–161.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Oscar H. Ibarra
    • 1
  • Tao Jiang
    • 2
  1. 1.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Department of Computer ScienceMcMaster UniversityHamiltonCanada

Personalised recommendations