1,094 research outputs found
Minimizing Running Costs in Consumption Systems
A standard approach to optimizing long-run running costs of discrete systems
is based on minimizing the mean-payoff, i.e., the long-run average amount of
resources ("energy") consumed per transition. However, this approach inherently
assumes that the energy source has an unbounded capacity, which is not always
realistic. For example, an autonomous robotic device has a battery of finite
capacity that has to be recharged periodically, and the total amount of energy
consumed between two successive charging cycles is bounded by the capacity.
Hence, a controller minimizing the mean-payoff must obey this restriction. In
this paper we study the controller synthesis problem for consumption systems
with a finite battery capacity, where the task of the controller is to minimize
the mean-payoff while preserving the functionality of the system encoded by a
given linear-time property. We show that an optimal controller always exists,
and it may either need only finite memory or require infinite memory (it is
decidable in polynomial time which of the two cases holds). Further, we show
how to compute an effective description of an optimal controller in polynomial
time. Finally, we consider the limit values achievable by larger and larger
battery capacity, show that these values are computable in polynomial time, and
we also analyze the corresponding rate of convergence. To the best of our
knowledge, these are the first results about optimizing the long-run running
costs in systems with bounded energy stores.Comment: 32 pages, corrections of typos and minor omission
Tableaux for Policy Synthesis for MDPs with PCTL* Constraints
Markov decision processes (MDPs) are the standard formalism for modelling
sequential decision making in stochastic environments. Policy synthesis
addresses the problem of how to control or limit the decisions an agent makes
so that a given specification is met. In this paper we consider PCTL*, the
probabilistic counterpart of CTL*, as the specification language. Because in
general the policy synthesis problem for PCTL* is undecidable, we restrict to
policies whose execution history memory is finitely bounded a priori.
Surprisingly, no algorithm for policy synthesis for this natural and
expressive framework has been developed so far. We close this gap and describe
a tableau-based algorithm that, given an MDP and a PCTL* specification, derives
in a non-deterministic way a system of (possibly nonlinear) equalities and
inequalities. The solutions of this system, if any, describe the desired
(stochastic) policies.
Our main result in this paper is the correctness of our method, i.e.,
soundness, completeness and termination.Comment: This is a long version of a conference paper published at TABLEAUX
2017. It contains proofs of the main results and fixes a bug. See the
footnote on page 1 for detail
Algorithmic randomness, reverse mathematics, and the dominated convergence theorem
We analyze the pointwise convergence of a sequence of computable elements of
L^1(2^omega) in terms of algorithmic randomness. We consider two ways of
expressing the dominated convergence theorem and show that, over the base
theory RCA_0, each is equivalent to the assertion that every G_delta subset of
Cantor space with positive measure has an element. This last statement is, in
turn, equivalent to weak weak K\"onig's lemma relativized to the Turing jump of
any set. It is also equivalent to the conjunction of the statement asserting
the existence of a 2-random relative to any given set and the principle of
Sigma_2 collection
Electronic Structure of Three-Dimensional Superlattices Subject to Tilted Magnetic Fields
Full quantum-mechanical description of electrons moving in 3D structures with
unidirectional periodic modulation subject to tilted magnetic fields requires
an extensive numerical calculation. To understand magneto-oscillations in such
systems it is in many cases sufficient to use the quasi-classical approach, in
which the zero-magnetic-field Fermi surface is considered as a
magnetic-field-independent rigid body in k-space and periods of oscillations
are related to extremal cross-sections of the Fermi surface cut by planes
perpendicular to the magnetic-field direction. We point out cases where the
quasi-classical treatment fails and propose a simple tight-binding
fully-quantum-mechanical model of the superlattice electronic structure.Comment: 8 pages, 7 figures, RevTex, submitted to Phys. Rev.
Infrared magneto-optical properties of (III,Mn)V ferromagetic semiconductors
We present a theoretical study of the infrared magneto-optical properties of
ferromagnetic (III,Mn)V semiconductors. Our analysis combines the kinetic
exchange model for (III,Mn)V ferromagnetism with Kubo linear response theory
and Born approximation estimates for the effect of disorder on the valence band
quasiparticles. We predict a prominent feature in the ac-Hall conductivity at a
frequency that varies over the range from 200 to 400 meV, depending on Mn and
carrier densities, and is associated with transitions between heavy-hole and
light-hole bands. In its zero frequency limit, our Hall conductivity reduces to
the -space Berry's phase value predicted by a recent theory of the
anomalous Hall effect that is able to account quantitatively for experiment. We
compute theoretical estimates for magnetic circular dichroism, Faraday
rotation, and Kerr effect parameters as a function of Mn concentration and free
carrier density. The mid-infrared response feature is present in each of these
magneto-optical effects.Comment: 11 pages, 5 figure
- …