On the complexity of (off-line) 1-tape ATM's running in constant reversals

  • Tao Jiang
Theory Of Computing, Algorithms And Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 468)


Yamamoto and Noguchi [YN87] raised the question of whether every recursively enumberable set can be accepted by a 1-tape or off-line 1-tape alternating Turing machine (ATM) whose (work)tape head makes only a constant number of reversals. In this paper, we answer the open question in the negative. We show that (1) constant-reversal 1-tape ATM's accept only regular languages and (2) there exists a recursive function h(k,r,n) such that for every k-state off-line 1-tape ATM M running in r reversals, the language accepted by M is in ASPACE(h(k,r,n)).

Key words

computational complexity alternating Turing machine 1-tape off-line 1-tape head reversal 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BB74]
    Baker, B. and R. Book, Reversal-bounded multipushdown machines, J. of Comput. System Sci. 8, 1974, pp. 315–332.Google Scholar
  2. [C81]
    Chan, T., Reversal complexity of counter machines, the Proceedings of the 13th Annual ACM Symposium on Theory of Computing, 1981, pp. 146–157.Google Scholar
  3. [CKS81]
    Chandra, A., D. Kozen, and L. Stockmeyer, Alternation, J. ACM 28, 1981, pp. 114–133.Google Scholar
  4. [CY87]
    Chen, J. and C. Yap, Reversal complexity, Proc. of 2nd IEEE Annual Conference on Structure in Complexity Theory, 1987, pp. 14–19.Google Scholar
  5. [F68]
    Fisher, P., The reduction of tape reversal for off-line one-tape Turing machines, J. of Comput. System Sci. 2, 1968, pp. 136–147.Google Scholar
  6. [GI81]
    Gurari, E. and O. Ibarra, The complexity of decision problems for finite-turn multicounter machines, J. of Comput. System Sci. 22, 1981, pp. 220–229.Google Scholar
  7. [G78]
    Greibach, S., Visits, crosses and reversal for nondeterministic off-line machines, Information and Control 36, pp. 174–216.Google Scholar
  8. [H68]
    Hartmanis, J., Tape-reversal bounded Turing machine computations, J. of Comput. System Sci. 2, 1968, pp. 117–135.Google Scholar
  9. [HU79]
    Hopcroft, J. and J. Ullman, Introduction to automata theory, languages, and computation, Addison-Wesley, 1979.Google Scholar
  10. [H85]
    Hromkovic, J., Alternating multicounter machines with constant number of reversals, Information Processing Letters 21, 1985, pp. 7–9.Google Scholar
  11. [H89]
    Hromkovic, J., Tradeoffs for language recognition on alternating machines, Theoretical Computer Science 63, 1989, pp. 203–221.Google Scholar
  12. [I78]
    Ibarra, O., Reversal-bounded multicounter machines and their decision problems, J. ACM 25, 1978, pp. 116–133.Google Scholar
  13. [IJ88]
    Ibarra, O. and T. Jiang, The power of alternating one-reversal counters and stacks, to appear in SIAM J. on Computing; also Proc. of 3rd IEEE Annual Conference on Structure in Complexity, 1988, pp. 70–77.Google Scholar
  14. [KV70]
    Kameda, T. and R. Vollmar, Note on tape reversal complexity of languages, Information and Control 17, 1970, pp. 203–215.Google Scholar
  15. [YN87]
    Yamamoto, H. and S. Noguchi, Comparison of the power between reversal-bounded ATMs and reversal-bounded NTMs, Information and Computation 75, 1987, pp. 144–161.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Tao Jiang
    • 1
  1. 1.Department of Computer Science and SystemsMcMaster UniversityHamiltonCanada

Personalised recommendations