Efficient deterministic finite automata split-minimization derived from Brzozowski's algorithm

Minimization of deterministic finite automata is a classic problem in Computer Science which is still studied nowadays. In this paper, we relate the different split-minimization methods proposed to date, or to be proposed, and the algorithm due to Brzozowski which has been usually set aside in any classification of DFA minimization algorithms. In our work, we first propose a polynomial minimization method derived from a paper by Champarnaud et al. We also show how the consideration of some efficiency improvements on this algorithm lead to obtain an algorithm similar to Hopcroft s classic algorithm. The results obtained lead us to propose a characterization of the set of possible splitters.García Gómez, P.; López Rodríguez, D.; Vázquez-De-Parga Andrade, M. (2014). Efficient deterministic finite automata split-minimization derived from Brzozowski's algorithm. International Journal of Foundations of Computer Science. 25(6):679-696. doi:10.1142/S0129054114500282S679696256Vázquez de Parga, M., García, P., & López, D. (2013). A polynomial double reversal minimization algorithm for deterministic finite automata. Theoretical Computer Science, 487, 17-22. doi:10.1016/j.tcs.2013.03.005Courcelle, B., Niwinski, D., & Podelski, A. (1991). A geometrical view of the determinization and minimization of finite-state automata. Mathematical Systems Theory, 24(1), 117-146. doi:10.1007/bf02090394POLÁK, L. (2005). MINIMALIZATIONS OF NFA USING THE UNIVERSAL AUTOMATON. International Journal of Foundations of Computer Science, 16(05), 999-1010. doi:10.1142/s0129054105003431Gries, D. (1973). Describing an algorithm by Hopcroft. Acta Informatica, 2(2). doi:10.1007/bf00264025Blum, N. (1996). An O(n log n) implementation of the standard method for minimizing n-state finite automata. Information Processing Letters, 57(2), 65-69. doi:10.1016/0020-0190(95)00199-9Knuutila, T. (2001). Re-describing an algorithm by Hopcroft. Theoretical Computer Science, 250(1-2), 333-363. doi:10.1016/s0304-3975(99)00150-

Detecting Electronic States at Stacking Faults in Magnetic Thin Films by Tunneling Spectroscopy

Co islands grown on Cu(111) with a stacking fault at the interface present a conductance in the empty electronic states larger than the Co islands that follow the stacking sequence of the Cu substrate. Electrons can be more easily injected into these faulted interfaces, providing a way to enhance transmission in future spintronic devices. The electronic states associated to the stacking fault are visualized by tunneling spectroscopy and its origin is identified by band structure calculations.Comment: 4 pages, 4 figures; to be published in Phys. Rev. Lett (2000

Periodically modulated geometric and electronic structure of graphene on Ru(0001)

We report here on a method to fabricate and characterize highly perfect, periodically rippled graphene monolayers and islands, epitaxially grown on single crystal metallic substrates under controlled UHV conditions. The periodicity of the ripples is dictated by the difference in lattice parameters of graphene and substrate, and, thus, it is adjustable. We characterize its perfection at the atomic scale by means of STM and determine its electronic structure in the real space by local tunnelling spectroscopy. There are periodic variations in the geometric and electronic structure of the graphene monolayer. We observe inhomogeneities in the charge distribution, i.e a larger occupied Density Of States at the higher parts of the ripples. Periodically rippled graphene might represent the physical realization of an ordered array of coupled graphene quantum dots. The data show, however, that for rippled graphene on Ru(0001) both the low and the high parts of the ripples are metallic. The fabrication of periodically rippled graphene layers with controllable characteristic length and different bonding interactions with the substrate will allow a systematic experimental test of this fundamental problem.Comment: 12 pages. Contribution to the topical issue on graphene of Semiconductor Science and Technolog

Lattice-matched versus lattice-mismatched models to describe epitaxial monolayer graphene on Ru (0001)

Monolayer graphene grown on Ru(0001) surfaces forms a superstructure with periodic modulations in its geometry and electronic structure. The large dimension and inhomogeneous features of this superstructure make its description and subsequent analysis a challenge for theoretical modeling based on density functional theory. In this work, we compare two different approaches to describe the same physical properties of this surface, focusing on the geometry and the electronic states confined at the surface. In the more complex approach, the actual moiré structure is taken into account by means of large unit cells, whereas in the simplest one, the graphene moiré is completely neglected by representing the system as a stretched graphene layer that adapts pseudomorphically to Ru(0001). As shown in previous work, the more complex model provides an accurate description of the existing experimental observations. More interestingly, we show that the simplified stretched models, which are computationally inexpensive, reproduce qualitatively the main features of the surface electronic structure. They also provide a simple and comprehensive picture of the observed electronic structure, thus making them particularly useful for the analysis of these and maybe other complex interfacesWe thank Barcelona Supercomputing Center–Spanish Supercomputing Network (BSC-RES) and Centro de Computación Científica – Universidad Autónoma de Madrid (CCC-UAM) for allocation of computer time. Work supported by the MICINN Projects No. FIS2010-15127, No. FIS2010-18847, No. CTQ2010-17006, No. FIS-2010-19609- C09-00, No. ACI2008-0777, No. 2010C-07-25200, and No. CSD2007-00010, the CAM program NANOBIOMAGNET S2009/MAT1726 and the Gobierno Vasco-UPV/EHU Project No. IT-366-07. S.B. acknowledges financial support from MEC under FPU Grant No. AP-2007-00157. D.S. acknowledges financial support from the FPI-UAM grant progra

Electron localization in epitaxial graphene on Ru(0001) determined by moiré corrugation

The interpretation of scanning tunneling spectroscopy (STS) and scanning tunneling microscopy measurements of epitaxial graphene on lattice-mismatched substrates is a challenging problem, because of the spatial modulation in the electronic structure imposed by the formation of a moiré pattern. Here we describe the electronic structure of graphene adsorbed on Ru(0001) by means of density functional theory calculations that include van der Waals interactions and are performed on a large 11×11 unit cell to account for the observed moiré patterns. Our results show the existence of localized electronic states in the high and low areas of the moiré at energies close to and well above the Fermi level, respectively. Localization is due to the spatial modulation of the graphene-Ru(0001) interaction and is at the origin of the various peaks observed in STS spectraWork supported by the MICINN Projects No. FIS2010-15127, No. FIS2010-18847, No. CTQ2010-17006, No. FIS-2010-19609-C09-00, No. ACI2008-0777, No. 2010C-07-25200, and No. CSD2007-00010, the CAM program NANOBIOMAGNET S2009/MAT1726, and the Gobierno Vasco-UPV/EHU Project No. IT-366-07. S.B. acknowledges financial support from MEC under FPU Grant No. AP-2007-0015

Role of dispersion forces in the structure of graphene monolayers on Ru surfaces

Elaborate density functional theory (DFT) calculations that include the effect of van der Waals (vdW) interactions have been carried out for graphene epitaxially grown on Ru(0001). The calculations predict a reduction of structural corrugation in the observed moiré pattern of about 25% (∼0.4  Å) with respect to DFT calculations without vdW corrections. The simulated STM topographies are close to the experimental ones in a wide range of bias voltage around the Fermi levelWe thank Mare Nostrum BSC and CCC-UAM for computer time. Work supported by the MICINN projects FIS2010-15127, FIS2010-18847, CTQ2010-17006, FIS2010-19609-C02-00, ACI2008-0777, 2010C-07- 25200, and CSD2007-00010, the CAM program NANOBIOMAGNET S2009/MAT1726, and the Gobierno Vasco—UPV/EHU project IT-366-0

Increasing the Rate of Magnesium Intercalation Underneath Epitaxial Graphene on 6H-SiC(0001)

Magnesium intercalated 'quasi-freestanding' bilayer graphene on 6H-SiC(0001) (Mg-QFSBLG) has many favorable properties (e.g., highly n-type doped, relatively stable in ambient conditions). However, intercalation of Mg underneath monolayer graphene is challenging, requiring multiple intercalation steps. Here, we overcome these challenges and subsequently increase the rate of Mg intercalation by laser patterning (ablating) the graphene to form micron-sized discontinuities. We then use low energy electron diffraction to verify Mg-intercalation and conversion to Mg-QFSBLG, and X-ray photoelectron spectroscopy to determine the Mg intercalation rate for patterned and non-patterned samples. By modeling Mg intercalation with the Verhulst equation, we find that the intercalation rate increase for the patterned sample is 4.5$\pm$1.7. Since the edge length of the patterned sample is $\approx$5.2 times that of the non-patterned sample, the model implies that the increased intercalation rate is proportional to the increase in edge length. Moreover, Mg intercalation likely begins at graphene discontinuities in pristine samples (not step edges or flat terraces), where the 2D-like crystal growth of Mg-silicide proceeds. Our laser patterning technique may enable the rapid intercalation of other atomic or molecular species, thereby expanding upon the library of intercalants used to modify the characteristics of graphene, or other 2D materials and heterostructures.Comment: 24 pages, 4 figure

Light emission from a scanning tunneling microscope: Fully retarded calculation

The light emission rate from a scanning tunneling microscope (STM) scanning a noble metal surface is calculated taking retardation effects into account. As in our previous, non-retarded theory [Johansson, Monreal, and Apell, Phys. Rev. B 42, 9210 (1990)], the STM tip is modeled by a sphere, and the dielectric properties of tip and sample are described by experimentally measured dielectric functions. The calculations are based on exact diffraction theory through the vector equivalent of the Kirchoff integral. The present results are qualitatively similar to those of the non-retarded calculations. The light emission spectra have pronounced resonance peaks due to the formation of a tip-induced plasmon mode localized to the cavity between the tip and the sample. At a quantitative level, the effects of retardation are rather small as long as the sample material is Au or Cu, and the tip consists of W or Ir. However, for Ag samples, in which the resistive losses are smaller, the inclusion of retardation effects in the calculation leads to larger changes: the resonance energy decreases by 0.2-0.3 eV, and the resonance broadens. These changes improve the agreement with experiment. For a Ag sample and an Ir tip, the quantum efficiency is $\approx$ 10$^{-4}$ emitted photons in the visible frequency range per tunneling electron. A study of the energy dissipation into the tip and sample shows that in total about 1 % of the electrons undergo inelastic processes while tunneling.Comment: 16 pages, 10 figures (1 ps, 9 tex, automatically included); To appear in Phys. Rev. B (15 October 1998

Scanning tunneling microscopy and spectroscopy at low temperatures of the (110) surface of Te doped GaAs single crystals

We have performed voltage dependent imaging and spatially resolved spectroscopy on the (110) surface of Te doped GaAs single crystals with a low temperature scanning tunneling microscope (STM). A large fraction of the observed defects are identified as Te dopant atoms which can be observed down to the fifth subsurface layer. For negative sample voltages, the dopant atoms are surrounded by Friedel charge density oscillations. Spatially resolved spectroscopy above the dopant atoms and above defect free areas of the GaAs (110) surface reveals the presence of conductance peaks inside the semiconductor band gap. The appearance of the peaks can be linked to charges residing on states which are localized within the tunnel junction area. We show that these localized states can be present on the doped GaAs surface as well as at the STM tip apex.Comment: 8 pages, 8 figures, accepted for publication in PR