Time and Space Bounds for Reversible Simulation

Details Time and Space Bounds for Reversible Simulation Time and Space Bounds for Reversible Simulation

2001-01-29

arxiv.org/abs/quant-ph/0101133v2

Journal of Physics A: Mathematical and General, 34(2001), 6821--6830.

Physics

Quantum Physics

11 pages LaTeX, Proc ICALP 2001, Lecture Notes in Computer Science, Vol xxx Springer-Verlag, Berlin, 2001

Scientific paper

10.1088/0305-4470/34/35/308

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.

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