Reversibility and Adiabatic Computation: Trading Time and Space for Energy
Abstract
Future miniaturization and mobilization of computing devices requires energy parsimonious `adiabatic' computation. This is contingent on logical reversibility of computation. An example is the idea of quantum computations which are reversible except for the irreversible observation steps. We propose to study quantitatively the exchange of computational resources like time and space for irreversibility in computations. Reversible simulations of irreversible computations are memory intensive. Such (polynomial time) simulations are analysed here in terms of `reversible' pebble games. We show that Bennett's pebbling strategy uses least additional space for the greatest number of simulated steps. We derive a tradeoff for storage space versus irreversible erasure. Next we consider reversible computation itself. An alternative proof is provided for the precise expression of the ultimate irreversibility cost of an otherwise reversible computation without restrictions on time and space use. A timeirreversibility tradeoff hierarchy in the exponential time region is exhibited. Finally, extreme timeirreversibility tradeoffs for reversible computations in the thoroughly unrealistic range of computable versus noncomputable timebounds are given.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 April 1996
 DOI:
 10.1098/rspa.1996.0039
 arXiv:
 arXiv:quantph/9703022
 Bibcode:
 1996RSPSA.452..769L
 Keywords:

 Quantum Physics;
 Computer Science  Computational Complexity;
 Computer Science  Computational Engineering;
 Finance;
 and Science;
 Computer Science  Data Structures and Algorithms
 EPrint:
 30 pages, Latex. Lemma 2.3 should be replaced by the slightly better ``There is a winning strategy with $n+2$ pebbles and $m1$ erasures for pebble games $G$ with $T_G= m2^n$, for all $m \geq 1$'' with appropriate further changes (as pointed out by Wim van Dam). This and further work on reversible simulations as in Section 2 appears in quantph/9703009