Time and Space Bounds for Reversible Simulation
We prove a general upper bound on the tradeoff between time and space that suffices for the reversible simulation of irreversible computation. Previously, only simulations using exponential time or quadratic space were known. The tradeoff shows for the first time that we can simultaneously achieve subexponential time and subquadratic space. The boundary values are the exponential time with hardly any extra space required by the Lange-McKenzie-Tapp method and the (log 3)th power time with square space required by the Bennett method. We also give the first general lower bound on the extra storage space required by general reversible simulation. This lower bound is optimal in that it is achieved by some reversible simulations.
KeywordsTuring Machine Exponential Time Space Bound Extra Space Quadratic Space
Unable to display preview. Download preview PDF.
- 5.M. Frank, T. Knight, and N. Margolus, Reversibility in optimally scalable computer architectures, Manuscript, MIT-LCS, 1997 //http://www.ai.mit.edu/~mpf/publications.html.
- 6.M.P. Frank and M.J. Ammer, Separations of reversible and irreversible space-time complexity classes, Submitted. //http://www.ai.mit.edu/~mpf/rc/memos/M06_oracle.html.
- 11.M. Li and P.M.B. Vitányi, Reversibility and adiabatic computation: trading time and space for energy, Proc. Royal Society of London, Series A, 452(1996), 769–789.Google Scholar
- 13.K. Morita, A. Shirasaki, and Y. Gono, A 1-tape 2-symbol reversible Turing machine, IEEE Trans. IEICE, E72 (1989), 223–228.Google Scholar
- 14.M. Nielsen, I. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000.Google Scholar
- 17.R. Williams, Space-Efficient Reversible Simulations, DIMACS REU report, July 2000. http://dimacs.rutgers.edu/~ryanw/