Abstract
We prove the first superlinear lower bound for a concrete, polynomial time recognizable decision problem on a Turing machine with one work tape and a two-way input tape (also called off-line 1-tape Turing machine).
In particular, for off-line Turing machines we show that two tapes are better than one and that three pushdown stores are better than two (both in the deterministic and in the nondeterministic case).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Alon andW. Maass, Meanders and their application in lower bound arguments.J. Comput. System Sci. 37 (1988), 118–129.
L. Babai, P. Pudlák, V. Rödl, andE. Szemerédi, Lower bounds to the complexity of symmetric boolean functions.Theoret. Comput. Sci. 74 (1990), 313–323.
M. Dietzfelbinger, The speed of copying on one-tape off-line turing machines.Inform. Process. Lett. 33 (1989), 83–89.
M. Dietzfelbinger and W. Maass, The complexity of matrix transposition on one-tape off-line turing machines with output tape, 1986. To appear inTheoret. Comput. Sci.
P. Duris, Z. Galil, W. J. Paul, and R. Reischuk, Two nonlinear bounds. InProc. Fifteenth Ann. ACM Symp. Theor. Comput., 1983, 127–132.
F. C. Hennie, One-tape off-line turing machine computations.Inform. and Control 8 (1965), 553–578.
J. E. Hopcroft and J. D. Ullman,Introduction to Automata Theory, Languages and Computation. Addison-Wesley, 1979.
M. Li andP. M. B. Vitanyi, Tape versus quene and stacks: the lower bounds.Inform. and Comput. 78 (1988), 56–85.
M. Li, L. Longpre, andP. M. B. Vitanyi, The power of the queue.Proc. of Structure in Complexity Theory, Lecture Notes in Computer Science 223 (1986), 219–233.
R. J. Lipton andR. E. Tarjan, A separator theorem for planar graphs.SIAM J. Appl. Math. 36 (1979), 177–189.
W. Maass, Combinatorial lower bound arguments for deterministic and nondeterministic turing machines.Trans. Amer. Math. Soc. 292 (1985), 675–693.
W. Maass andG. Schnitger, An optimal lower bound for turing machines with one work tape and a two-way input tape.Proc. of Structure in Complexity Theory, Lecture Notes in Computer Science 223 (1986), 249–264.
W. Maass, G. Schnitger, and E.Szemerédi, Two tapes are better than one for off-line turing machines. InProc. Nineteenth Ann. ACM Symp. Theor. Comput., 1987, 94–100.
W. J. Paul, N. Pippenger, E. Szemerédi, and W. Trotter, On determinism versus nondeterminism and related problems. InProc. 24th Ann. Symp. Found. Comput. Sci., 1983, 429–438.
M. O. Rabin, Real time computation.Israel J. of Math. 1 (1963), 203–211.
J.E. Savage, The performance of multilective vlsi algorithms.J. Comput. System Sci. 29 (1984), 243–272.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Maass, W., Schnitger, G., Szemerédi, E. et al. Two tapes versus one for off-line Turing machines. Comput Complexity 3, 392–401 (1993). https://doi.org/10.1007/BF01275490
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01275490