Abstract
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.
All authors are partially supported by the EU fifth framework project QAIP, IST1999-11234, the NoE QUIPROCONE IST-1999-29064, the ESF QiT Programmme, and the EU Fourth Framework BRA NeuroCOLT II Working Group EP 27150. Buhrman and Vitényi are also affiliated with the University of Amsterdam. Tromp is also affiliated with Bioinformatics Solutions, Waterloo, N2L 3G1 Ontario, Canada.
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References
C.H. Bennett. Logical reversibility of computation. IBM J. Res. Develop., 17:525–532, 1973.
C.H. Bennett. The thermodynamics of computation—a review. Int. J. Theoret. Phys., 21(1982), 905–940.
C.H. Bennett. Time-space tradeoffs for reversible computation. SIAM J. Comput., 18(1989), 766–776.
E. Fredkin and T. Toffoli. Conservative logic. Int. J. Theoret. Phys., 21(1982),219–253.
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.
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.
R.W. Keyes, IBM J. Res. Dev., 32(1988), 24–28.
R. Landauer. Irreversibility and heat generation in the computing process. IBM J. Res. Develop., 5:183–191, 1961.
K.J. Lange, P. McKenzie, and A. Tapp, Reversible space equals deterministic space, J. Comput. System Sci., 60:2(2000), 354–367.
R.Y. Levine and A.T. Sherman, A note on Bennett’s time-space tradeoff for reversible computation, SIAM J. Comput., 19:4(1990), 673–677.
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.
M. Li, J. Tromp, and P. Vitányi, Reversible simulation of irreversible computation. Physica D, 120(1998) 168–176.
K. Morita, A. Shirasaki, and Y. Gono, A 1-tape 2-symbol reversible Turing machine, IEEE Trans. IEICE, E72 (1989), 223–228.
M. Nielsen, I. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000.
P.W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput., 26:5(1997), 1484–1509.
M. Sipser, Halting space-bounded computation, Theoret. Comp. Sci., 10(1990), 335–338.
R. Williams, Space-Efficient Reversible Simulations, DIMACS REU report, July 2000. http://dimacs.rutgers.edu/~ryanw/
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Buhrman, H., Tromp, J., Vitányi, P. (2001). Time and Space Bounds for Reversible Simulation. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_82
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DOI: https://doi.org/10.1007/3-540-48224-5_82
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