On the Complexity of Case-Based Planning

We analyze the computational complexity of problems related to case-based planning: planning when a plan for a similar instance is known, and planning from a library of plans. We prove that planning from a single case has the same complexity than generative planning (i.e., planning "from scratch"); using an extended definition of cases, complexity is reduced if the domain stored in the case is similar to the one to search plans for. Planning from a library of cases is shown to have the same complexity. In both cases, the complexity of planning remains, in the worst case, PSPACE-complete

Universal oscillations in counting statistics

Noise is a result of stochastic processes that originate from quantum or classical sources. Higher-order cumulants of the probability distribution underlying the stochastic events are believed to contain details that characterize the correlations within a given noise source and its interaction with the environment, but they are often difficult to measure. Here we report measurements of the transient cumulants > of the number n of passed charges to very high orders (up to m=15) for electron transport through a quantum dot. For large m, the cumulants display striking oscillations as functions of measurement time with magnitudes that grow factorially with m. Using mathematical properties of high-order derivatives in the complex plane we show that the oscillations of the cumulants in fact constitute a universal phenomenon, appearing as functions of almost any parameter, including time in the transient regime. These ubiquitous oscillations and the factorial growth are system-independent and our theory provides a unified interpretation of previous theoretical studies of high-order cumulants as well as our new experimental data.Comment: 19 pages, 4 figures, final version as published in PNA

Time-Resolved Two-Photon Quantum Interference

The interference of two independent single-photon pulses impinging on a beam splitter is analysed in a generalised time-resolved manner. Different aspects of the phenomenon are elaborated using different representations of the single-photon wave packets, like the decomposition into single-frequency field modes or spatio-temporal modes matching the photonic wave packets. Both representations lead to equivalent results, and a photon-by-photon analysis reveals that the quantum-mechanical two-photon interference can be interpreted as a classical one-photon interference once a first photon is detected. A novel time-dependent quantum-beat effect is predicted if the interfering photons have different frequencies. The calculation also reveals that full two-photon fringe visibility can be achieved under almost any circumstances by applying a temporal filter to the signal.Comment: 6 pages, 4 figure

Exact Kohn-Sham exchange kernel for insulators and its long-wavelength behavior

We present an exact expression for the frequency-dependent Kohn-Sham exact-exchange (EXX) kernel for periodic insulators, which can be employed for the calculation of electronic response properties within time-dependent (TD) density-functional theory. It is shown that the EXX kernel has a long-wavelength divergence behavior of the exact full exchange-correlation kernel and thus rectifies one serious shortcoming of the adiabatic local-density approximation and generalized-gradient approximations kernels. A comparison between the TDEXX and the GW-approximation-Bethe-Salpeter-equation approach is also made.Comment: two column format 6 pages + 1 figure, to be publisehd in Physical Review

Compilability of Abduction

Abduction is one of the most important forms of reasoning; it has been successfully applied to several practical problems such as diagnosis. In this paper we investigate whether the computational complexity of abduction can be reduced by an appropriate use of preprocessing. This is motivated by the fact that part of the data of the problem (namely, the set of all possible assumptions and the theory relating assumptions and manifestations) are often known before the rest of the problem. In this paper, we show some complexity results about abduction when compilation is allowed

Unscreened Hartree-Fock calculations for metallic Fe, Co, Ni, and Cu from ab-initio Hamiltonians

Unscreened Hartree-Fock approximation (HFA) calculations for metallic Fe, Co, Ni, and Cu are presented, by using a quantum-chemical approach. We believe that these are the first HFA results to have been done for crystalline 3d transition metals. Our approach uses a linearized muffin-tin orbital calculation to determine Bloch functions for the Hartree one-particle Hamiltonian, and from these obtains maximally localized Wannier functions, using a method proposed by Marzari and Vanderbilt. Within this Wannier basis all relevant one-particle and two-particle Coulomb matrix elements are calculated. The resulting second-quantized multi-band Hamiltonian with ab-initio parameters is studied within the simplest many-body approximation, namely the unscreened, self-consistent HFA, which takes into account exact exchange and is free of self-interactions. Although the d-bands sit considerably lower within HFA than within the local (spin) density approximation L(S)DA, the exchange splitting and magnetic moments for ferromagnetic Fe, Co, and Ni are only slightly larger in HFA than what is obtained either experimentally or within LSDA. The HFA total energies are lower than the corresponding LSDA calculations. We believe that this same approach can be easily extended to include more sophisticated ab-initio many-body treatments of the electronic structure of solids.Comment: 11 papes, 7 figures, 5 table

Density-functional Study of Small Molecules within the Krieger-Li-Iafrate Approximation

We report density-functional studies of several small molecules ($H_{2}, N_{2}, CO, H_{2}O$, and $CH_{4}$) within the Krieger-Li-Iafrate (KLI) approximation to the exact Kohn-Sham local exchange potential, using a three-dimensional real-space finite-difference pseudopotential method. It is found that exchange-only KLI leads to markedly improved eigenvalue spectra compared to those obtained within the standard local-density approximation (LDA), the generalized gradient approximation (GGA), and the Hartree-Fock (HF) method. For structural properties, exchange-only KLI results are close to the corresponding HF values. We find that the addition of LDA or GGA correlation energy functionals to the KLI exact exchange energy functional does not lead to systematic improvements.Comment: 16 pages including 1 fugure, to be published in Phys. Rev. A Nov. 1 '9

Partial Weighted MaxSAT for Optimal Planning

Abstract. We consider the problem of computing optimal plans for proposi-tional planning problems with action costs. In the spirit of leveraging advances in general-purpose automated reasoning for that setting, we develop an approach that operates by solving a sequence of partial weighted MaxSAT problems, each of which corresponds to a step-bounded variant of the problem at hand. Our ap-proach is the first SAT-based system in which a proof of cost-optimality is ob-tained using a MaxSAT procedure. It is also the first system of this kind to incor-porate an admissible planning heuristic. We perform a detailed empirical eval-uation of our work using benchmarks from a number of International Planning Competitions.