Tradeoffs for language recognition on parallel computing models

  • Juraj Hromkovič
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 226)


The alternating machine having a separate input tape with k two-way, read-only heads, and a certain number of internal configurations — AM(k) is considered as a parallel computing model. For the complexity measure TIME·SPACE·PARALLELISM (TSP), the optimal lower bounds ω(n2) and ω (n3/2) resp. are proved for the recognition of specific languages on AM (1), and AM(k) respectively. For the complexity measure REVERSALS·SPACE·PARALLELISM (RSP), the lower bound ω(n1/3/log2n) is established for the recognition of a specific language on AM(k). This result implies a polynomial lower bound on PTIME·HARDWARE of parallel RAM's. All lower bounds obtained are substantially improved for the case that SPACE ≥nɛ, for 0 < ɛ < 1. Several strongest lower bounds for two-way (and one-way) alternating (deterministic, and nondeterministic) multihead finite automata are obtained as direct consequences of these results.


Turing Machine Complexity Measure Specific Language Finite Automaton Universal State 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Borodin,A.B. — Cook,S.A. (1980), A time-space tradeoff for sorting on a general model of computation. Proc. 12th ACM STOC, pp.294–301.Google Scholar
  2. 2.
    Chandra, A.K. — Kozen, D.C. — Stockmeyer, L.J. (1981), Alternation. J. ACM 28, 1, pp.114–133.Google Scholar
  3. 3.
    Cobham,A. (1966), The recognition problem for perfect squares. Proc. 7th IEEE Symp. on SWAT, Berkeley, pp.78–87.Google Scholar
  4. 4.
    Ďuriš, P. — Galil, Z. (1984), A time-space tradeoff for language recognition. Math. Syst. Theory 17, pp.3–12.Google Scholar
  5. 5.
    Ďurisš,P. — Galil,Z. — Paul,W. — Reischuk,R. (1983), Two nonlinear lower bounds. Proc. 15th ACM STOC, pp.127–132.Google Scholar
  6. 6.
    Dymond,P.W. — Cook,S.A. (1980), Hardware complexity and parallel computation. Proc. 21th IEEE FOCS, pp.360–372.Google Scholar
  7. 7.
    Freiwalds,R. (1984), Quadratic lower bound for nondeterministic Turing machines. Short, unpublished communication at the 11th MFCS'84.Google Scholar
  8. 8.
    Hromkovič, J. (1983), One-way multihead deterministic finite automata. Acta Informat. 19, 377–384.Google Scholar
  9. 9.
    Hromkovič, J. (1985), On the power of alternation in automata theory. J. Comput. System Sciences 31, No. 1, 28–39.Google Scholar
  10. 10.
    Hromkovič, J. (1985), Fooling a two-way multihead automaton with reversal number restriction. Acta Informat. 22, 589–594.Google Scholar
  11. 11.
    Janiga, L. (1979), Real-time computations of two-way multihead finite automata. Prof. FCT'79, L. Budach ed., Academic Verlag, Berlin 1979, pp.214–219.Google Scholar
  12. 12.
    King, K.N. (1981), Alternating multihead finite automata. Proc. 8th ICALP, Lecture Notes in Computer Science 115, Springer-Verlag, Berlin-Heidelberg-New York 1981.Google Scholar
  13. 13.
    Maas, W. (1984), Quadratic lower bounds for deterministic and nondeterministic one-tape Turing machines. Proc. 16th ACM STOC, pp.401–408.Google Scholar
  14. 14.
    Matsuno, H. — Inoue, K. — Tanigushi, H. — Takanami, I. (1985), Alternating simple multihead finite automata, Theoret. Comput. Sci. 36, 299–308.Google Scholar
  15. 15.
    Ito, A. — Inoue, K. — Takanami, I. — Tanigushi, H. (1982), Two-dimensional alternating Turing machines with only universal states. Inform. Control 55, Nos. 1–3, 193–221.Google Scholar
  16. 16.
    Inoue, K. — Takanami, I. — Tanigushi, H. (1983), Two-dimensional alternating Turing machines. Theoret. Comput. Science 27, 61–83.Google Scholar
  17. 17.
    Inoue, K. — Ito, A. — Takanami, I. — Tanigushi, H. (1985), A spacehierarchy results on two-dimensional alternating Turing machines with only universal states. Information Sciences 35, 79–90.Google Scholar
  18. 18.
    Li, M. (1984), On one tape versus two stacks. Technical Report 84-591, January 1984, Dept. of Comput. Sci., Cornell University, Ithaca, New York.Google Scholar
  19. 19.
    Rivest, R.L. — Yao, A.C. (1978), k+1 heads are better than k, J. ACM 25, 2, 337–340.Google Scholar
  20. 20.
    Sudborough, I.H. (1974), Bounded-reversal multihead finite automata languages. Informat. Control 25, pp.317–328.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Juraj Hromkovič
    • 1
  1. 1.Dept. of Theoretical Cybernetics and Mathematical InformaticsComenius UniversityBratislavaCzechoslovakia

Personalised recommendations