211,420 research outputs found
Energy-Efficient Circuit Design
We initiate the theoretical investigation of energy-efficient circuit design.
We assume that the circuit design specifies the circuit layout as well as the
supply voltages for the gates. To obtain maximum energy efficiency, the circuit
design must balance the conflicting demands of minimizing the energy used per gate,
and minimizing the number of gates in the circuit; If the energy supplied to the
gates is small, then functional failures are likely, necessitating a circuit layout
that is more fault-tolerant, and thus that has more gates.
By leveraging previous
work on fault-tolerant circuit design, we show general upper and lower bounds on
the amount of energy required by a circuit to compute a given relation. We show
that some circuits would be asymptotically more energy-efficient if heterogeneous
supply voltages were allowed, and show that for some circuits the most energy-efficient
supply voltages are homogeneous over all gates.
In the traditional approach to circuit design the
supply voltages for each transistor/gate are set sufficiently high so that with
sufficiently high probability no transistor fails.
We show that if there is a better (in terms of worst-case relative error with respect to energy) method than the traditional approach
then ,
and thus there is a complexity theoretic obstacle to achieving energy savings with Near-Threshold computing.
We show that almost all
Boolean functions require circuits that use exponential energy. This is not an immediate
consequence of Shannon's classic result that most functions require exponential
sized circuits of faultless gates because, as we show, the same circuit layout can
compute many different functions, depending on the value of the supply voltage.
If the error bound must vanish as the number of inputs increases, we show that a natural class of functions can be computed with asymptotically less energy using heterogeneous supply voltages than is possible using homogeneous supply voltages.
We also prove upper bounds on the asymptotic energy savings achieved by using heterogeneous supply voltages over homogeneous supply voltages for a class of functions, and also show a relation that can bypass this bound
Quantum harmonic oscillator systems with disorder
We study many-body properties of quantum harmonic oscillator lattices with
disorder. A sufficient condition for dynamical localization, expressed as a
zero-velocity Lieb-Robinson bound, is formulated in terms of the decay of the
eigenfunction correlators for an effective one-particle Hamiltonian. We show
how state-of-the-art techniques for proving Anderson localization can be used
to prove that these properties hold in a number of standard models. We also
derive bounds on the static and dynamic correlation functions at both zero and
positive temperature in terms of one-particle eigenfunction correlators. In
particular, we show that static correlations decay exponentially fast if the
corresponding effective one-particle Hamiltonian exhibits localization at low
energies, regardless of whether there is a gap in the spectrum above the ground
state or not. Our results apply to finite as well as to infinite oscillator
systems. The eigenfunction correlators that appear are more general than those
previously studied in the literature. In particular, we must allow for
functions of the Hamiltonian that have a singularity at the bottom of the
spectrum. We prove exponential bounds for such correlators for some of the
standard models
Explicitly correlated trial wave functions in Quantum Monte Carlo calculations of excited states of Be and Be-
We present a new form of explicitly correlated wave function whose parameters
are mainly linear, to circumvent the problem of the optimization of a large
number of non-linear parameters usually encountered with basis sets of
explicitly correlated wave functions. With this trial wave function we
succeeded in minimizing the energy instead of the variance of the local energy,
as is more common in quantum Monte Carlo methods. We applied this wave function
to the calculation of the energies of Be 3P (1s22p2) and Be- 4So (1s22p3) by
variational and diffusion Monte Carlo methods. The results compare favorably
with those obtained by different types of explicitly correlated trial wave
functions already described in the literature. The energies obtained are
improved with respect to the best variational ones found in literature, and
within one standard deviation from the estimated non-relativistic limitsComment: 19 pages, no figures, submitted to J. Phys.
Percentile Queries in Multi-Dimensional Markov Decision Processes
Markov decision processes (MDPs) with multi-dimensional weights are useful to
analyze systems with multiple objectives that may be conflicting and require
the analysis of trade-offs. We study the complexity of percentile queries in
such MDPs and give algorithms to synthesize strategies that enforce such
constraints. Given a multi-dimensional weighted MDP and a quantitative payoff
function , thresholds (one per dimension), and probability thresholds
, we show how to compute a single strategy to enforce that for all
dimensions , the probability of outcomes satisfying is at least . We consider classical quantitative payoffs from
the literature (sup, inf, lim sup, lim inf, mean-payoff, truncated sum,
discounted sum). Our work extends to the quantitative case the multi-objective
model checking problem studied by Etessami et al. in unweighted MDPs.Comment: Extended version of CAV 2015 pape
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