51,116 research outputs found
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
Energy-Efficient Algorithms
We initiate the systematic study of the energy complexity of algorithms (in
addition to time and space complexity) based on Landauer's Principle in
physics, which gives a lower bound on the amount of energy a system must
dissipate if it destroys information. We propose energy-aware variations of
three standard models of computation: circuit RAM, word RAM, and
transdichotomous RAM. On top of these models, we build familiar high-level
primitives such as control logic, memory allocation, and garbage collection
with zero energy complexity and only constant-factor overheads in space and
time complexity, enabling simple expression of energy-efficient algorithms. We
analyze several classic algorithms in our models and develop low-energy
variations: comparison sort, insertion sort, counting sort, breadth-first
search, Bellman-Ford, Floyd-Warshall, matrix all-pairs shortest paths, AVL
trees, binary heaps, and dynamic arrays. We explore the time/space/energy
trade-off and develop several general techniques for analyzing algorithms and
reducing their energy complexity. These results lay a theoretical foundation
for a new field of semi-reversible computing and provide a new framework for
the investigation of algorithms.Comment: 40 pages, 8 pdf figures, full version of work published in ITCS 201
Toward an Energy Efficient Language and Compiler for (Partially) Reversible Algorithms
We introduce a new programming language for expressing reversibility,
Energy-Efficient Language (Eel), geared toward algorithm design and
implementation. Eel is the first language to take advantage of a partially
reversible computation model, where programs can be composed of both reversible
and irreversible operations. In this model, irreversible operations cost energy
for every bit of information created or destroyed. To handle programs of
varying degrees of reversibility, Eel supports a log stack to automatically
trade energy costs for space costs, and introduces many powerful control logic
operators including protected conditional, general conditional, protected
loops, and general loops. In this paper, we present the design and compiler for
the three language levels of Eel along with an interpreter to simulate and
annotate incurred energy costs of a program.Comment: 17 pages, 0 additional figures, pre-print to be published in The 8th
Conference on Reversible Computing (RC2016
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
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 ()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.Comment: 11 pages LaTeX, Proc ICALP 2001, Lecture Notes in Computer Science,
Vol xxx Springer-Verlag, Berlin, 200
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