2,343 research outputs found
Reversible Simulation of Irreversible Computation by Pebble Games
Reversible simulation of irreversible algorithms is analyzed in the stylized
form of a `reversible' pebble game. While such simulations incur little
overhead in additional computation time, they use a large amount of additional
memory space during the computation. The reacheable reversible simulation
instantaneous descriptions (pebble configurations) are characterized
completely. As a corollary we obtain the reversible simulation by Bennett and
that among all simulations that can be modelled by the pebble game, Bennett's
simulation is optimal in that it uses the least auxiliary space for the
greatest number of simulated steps. One can reduce the auxiliary storage
overhead incurred by the reversible simulation at the cost of allowing limited
erasing leading to an irreversibility-space tradeoff. We show that in this
resource-bounded setting the limited erasing needs to be performed at precise
instants during the simulation. We show that the reversible simulation can be
modified so that it is applicable also when the simulated computation time is
unknown.Comment: 11 pages, Latex, Submitted to Physica
Reversibility and Adiabatic Computation: Trading Time and Space for Energy
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 trade-off 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 time-irreversibility trade-off hierarchy
in the exponential time region is exhibited. Finally, extreme
time-irreversibility trade-offs for reversible computations in the thoroughly
unrealistic range of computable versus noncomputable time-bounds are given.Comment: 30 pages, Latex. Lemma 2.3 should be replaced by the slightly better
``There is a winning strategy with pebbles and erasures for
pebble games with , for all '' with appropriate
further changes (as pointed out by Wim van Dam). This and further work on
reversible simulations as in Section 2 appears in quant-ph/970300
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