On the power of several queues
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.
Unable to display preview. Download preview PDF.
- [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
- [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
- [Cal88]Cristian Calude. Theories of Computational Complexity, volume 35 of Annals of Discrete Mathematics. Elsevier North-Holland, Amsterdam, 1988.Google Scholar
- [Hen66]Frederick C. Hennie. On-line Turing machine computations. IEEE Transactions on Electronic Computers, 15:35–44, 1966.Google Scholar
- [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
- [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
- [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
- [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
- [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
- [Rab63]Michael O. Rabin. Real time computation. Israel Journal of Mathematics, 1:203–211, 1963.Google Scholar