On the power of several queues

  • Martin Schmidt
Automata And Formal Languages
Part of the Lecture Notes in Computer Science book series (LNCS, volume 480)


We present almost matching upper and lower time bounds for the simulation of Turing machines with many queues (resp. tapes, stacks) on Turing machines with few queues. In particular the power of two queues in comparison with other storage types is clarified, which resolves a question left open by [LLV86]. We show: Multistorage Turing machines can be simulated in time O(t(n)1+1/k) on k-queue machines. Every online simulation of k+1 queues (or of two tapes) on k queues requires time Ω(t(n)1+1/k/polylogt(n)). The lower bounds are based on Kolmogorov complexity.


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  1. [Aan74]
    Stål O. Aanderaa. On k-tape versus (k − 1)-tape real time computation. In SIAM-AMS Proceedings, volume 7: Complexity of Computation, pages 75–96, 1974.Google Scholar
  2. [BDG90]
    José Luis Balcázar, Josep Dáz, and Joaquim Gabarró. Structural Complexity, volume 11 and 22 of EATCS Monographs on Theoretical Computer Science. Springer, Berlin, 1988–90.Google Scholar
  3. [Cal88]
    Cristian Calude. Theories of Computational Complexity, volume 35 of Annals of Discrete Mathematics. Elsevier North-Holland, Amsterdam, 1988.Google Scholar
  4. [ĎGPR84]
    Pavol Ďūriš, Zvi Galil, Wolfgang Johannes Paul, and Karl Rüdiger Reischuk. Two nonlinear lower bounds. Information and Control, 60:1–11, 1984.CrossRefGoogle Scholar
  5. [Die90]
    Martin Dietzfelbinger. The speed of copying on one-tape off-line Turing machines. Information Processing Letters, 33:83–89, 1989/90.CrossRefGoogle Scholar
  6. [Hen65]
    Frederick C. Hennie. One-tape, off-line Turing machine computations. Information and Control, 8:553–578, 1965.CrossRefGoogle Scholar
  7. [Hen66]
    Frederick C. Hennie. On-line Turing machine computations. IEEE Transactions on Electronic Computers, 15:35–44, 1966.Google Scholar
  8. [HS65]
    Juris Hartmanis and Richard E. Stearns. On the computational complexity of algorithms. Transactions of the American Mathematical Society, 117:285–306, 1965.Google Scholar
  9. [HS66]
    Frederick C. Hennie and Richard E. Stearns. Two-tape simulation of multitape Turing machines. Journal of the ACM, 13:533–546, 1966.CrossRefGoogle Scholar
  10. [Li88]
    Ming Li. Simulating two pushdown stores by one tape in \(O(n^{1.5} \sqrt {\log n} )\) time. Journal of Computer and System Sciences, 37:101–116, 1988. also: 26th FOCS 1985.CrossRefGoogle Scholar
  11. [LLV86]
    Ming Li, Luc Longpré, and Paul M. B. Vitányi. The power of the queue. In 1 st Structure in Complexity Theory, pages 219–233. ACM, IEEE, 1986.Google Scholar
  12. [LV88]
    Ming Li and Paul M. B. Vitányi. Tape versus queue and stacks: The lower bounds. Information and Computation, 78:56–85, 1988.CrossRefGoogle Scholar
  13. [LV90]
    Ming Li and Paul M. B. Vitányi. Kolmogorov complexity and its applications. In Jan van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A: Algorithms and Complexity, pages 187–254. Elsevier North-Holland, Amsterdam, 1990.Google Scholar
  14. [Maa85]
    Wolfgang Maass. Combinatorial lower bound arguments for deterministic and nondeterministic Turing machines. Transactions of the American Mathematical Society, 292:675–693, 1985.Google Scholar
  15. [MSS87]
    Wolfgang Maass, Georg Schnitger, and Endre Szemerédi. Two tapes are better than one for off-line Turing machines. In 19 th STOC, pages 94–100. ACM, 1987.Google Scholar
  16. [Pau82]
    Wolfgang Johannes Paul. On-line simulation of k+1 tapes by k tapes requires nonlinear time. Information and Control, 53:1–8, 1982.CrossRefGoogle Scholar
  17. [PSS81]
    Wolfgang Johannes Paul, Joel I. Seiferas, and Janos Simon. An information theoretic approach to time bounds for on-line computation. Journal of Computer and System Sciences, 23:108–126, 1981.CrossRefGoogle Scholar
  18. [Rab63]
    Michael O. Rabin. Real time computation. Israel Journal of Mathematics, 1:203–211, 1963.Google Scholar
  19. [Vit84]
    Paul M. B. Vitányi. On two-tape real-time computation and queues. Journal of Computer and System Sciences, 29:303–311, 1984.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  1. 1.InformatikUniversität DortmundBRD

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