Abstract
Paul and Reischuk devised space efficient simulations of logarithmic cost random access machines and multidimensional Turing machines. We simplify their general space reduction technique and extend it to other computational models, including pointer machines, which model computations on graphs and data structures. Every pointer machine of time complexityT(n) can be simulated by a pointer machine of space complexityO(T(n)/logT(n)).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adleman, L. M., and Loui, M. C. (1981), Space-bounded simulation of multitape Turing machines,Math. Systems Theory 14, 215–222.
Bentley, J. L., and Brown, D. J. (1982), A general class of resource trade-offs,J. Comput. System Sci. 25, 214–238.
Borodin, A., and Cook, S. (1982), A time-space tradeoff for sorting on a general sequential model of computation,SIAM J. Comput. 11, 287–297.
Dymond, P. W., and Tompa, M. (1985), Speedups of deterministic machines by synchronous parallel machines,J. Comput. System Sci. 30, 149–161.
Hopcroft, J., Paul, W., and Valiant, L. (1977). On time versus space,J. Assoc. Comput. Mach. 24 332–337.
Hopcroft, J. E., and Ullman, J. D. (1968), Relations between time and tape complexities,J. Assoc. Comput. Mach. 15, 414–427.
Hopcroft, J. E., and Ullman, J. D. (1979),Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, Mass.
Loui, M. C. (1981), A space bound for one-tape multidimensional Turing machines,Theoret. Comput. Sci. 15, 311–320.
Meyer, A. R., and Shamos, M. I. (1977), Time and space, inPerspectives on Computer Science, ed. A. K. Jones, Academic Press, New York, pp. 125–146.
Paterson, M. S. (1972), Tape bounds for time-bounded Turing machines,J. Comput. System Sci. 6, 116–124.
Paterson, M. S., Fischer, M. J., and Meyer, A. R. (1974), An improved overlap argument for on-line multiplication,SIAM-AMS Proceedings, 7, Amer. Math. Soc., Providence, R.I., pp. 97–111.
Paul, W., and Reischuk, R. (1981), On time versus space II,J. Comput. System Sci. 22, 312–327.
Schönhage, A. (1980), Storage modification machines,SIAM J. Comput. 9, 490–508.
Tarjan, R. E. (1979), A class of algorithms which require nonlinear time to maintain disjoint sets,J. Comput. System Sci. 18, 110–127.
Tompa, M. (1980), Time-space tradeoffs for computing functions, using connectivity properties of their circuits.J. Comput. System Sci. 20, 118–132.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Halpern, J.Y., Loui, M.C., Meyer, A.R. et al. On time versus space III. Math. Systems Theory 19, 13–28 (1986). https://doi.org/10.1007/BF01704903
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01704903