Two-Way Automata Making Choices Only at the Endmarkers

The question of the state-size cost for simulation of two-way nondeterministic automata (2NFAs) by two-way deterministic automata (2DFAs) was raised in 1978 and, despite many attempts, it is still open. Subsequently, the problem was attacked by restricting the power of 2DFAs (e.g., using a restricted input head movement) to the degree for which it was already possible to derive some exponential gaps between the weaker model and the standard 2NFAs. Here we use an opposite approach, increasing the power of 2DFAs to the degree for which it is still possible to obtain a subexponential conversion from the stronger model to the standard 2DFAs. In particular, it turns out that subexponential conversion is possible for two-way automata that make nondeterministic choices only when the input head scans one of the input tape endmarkers. However, there is no restriction on the input head movement. This implies that an exponential gap between 2NFAs and 2DFAs can be obtained only for unrestricted 2NFAs using capabilities beyond the proposed new model. As an additional bonus, conversion into a machine for the complement of the original language is polynomial in this model. The same holds for making such machines self-verifying, halting, or unambiguous. Finally, any superpolynomial lower bound for the simulation of such machines by standard 2DFAs would imply LNL. In the same way, the alternating version of these machines is related to L =? NL =? P, the classical computational complexity problems.Comment: 23 page

An In-Place Sorting with O(n log n) Comparisons and O(n) Moves

We present the first in-place algorithm for sorting an array of size n that performs, in the worst case, at most O(n log n) element comparisons and O(n) element transports. This solves a long-standing open problem, stated explicitly, e.g., in [J.I. Munro and V. Raman, Sorting with minimum data movement, J. Algorithms, 13, 374-93, 1992], of whether there exists a sorting algorithm that matches the asymptotic lower bounds on all computational resources simultaneously

Formalism and quality of a proper motion link with extragalactic objects for astrometric satellite missions

The accuracy of the link of the proper motion system of astrometric satellite missions like AMEX and GAIA is discussed. Monte-Carlo methods were used to simulate catalogues of positions and proper motions of quasars and galaxies to test the link. The main conclusion is, that future satellite missions like GAIA may be ``self-calibrated'' by their measurements of QSOs, while additional measurements from radio stars or HST-data are needed to calibrate the less deep reaching astrometric satellite missions of AMEX type.Comment: Accepted for publication in A&A, LaTeX A&A style, 7 pages, 4 figure

Translation from Classical Two-Way Automata to Pebble Two-Way Automata

We study the relation between the standard two-way automata and more powerful devices, namely, two-way finite automata with an additional "pebble" movable along the input tape. Similarly as in the case of the classical two-way machines, it is not known whether there exists a polynomial trade-off, in the number of states, between the nondeterministic and deterministic pebble two-way automata. However, we show that these two machine models are not independent: if there exists a polynomial trade-off for the classical two-way automata, then there must also exist a polynomial trade-off for the pebble two-way automata. Thus, we have an upward collapse (or a downward separation) from the classical two-way automata to more powerful pebble automata, still staying within the class of regular languages. The same upward collapse holds for complementation of nondeterministic two-way machines. These results are obtained by showing that each pebble machine can be, by using suitable inputs, simulated by a classical two-way automaton with a linear number of states (and vice versa), despite the existing exponential blow-up between the classical and pebble two-way machines

Compton spectra of atoms at high x-ray intensity

Compton scattering is the nonresonant inelastic scattering of an x-ray photon by an electron and has been used to probe the electron momentum distribution in gas-phase and condensed-matter samples. In the low x-ray intensity regime, Compton scattering from atoms dominantly comes from bound electrons in neutral atoms, neglecting contributions from bound electrons in ions and free (ionized) electrons. In contrast, in the high x-ray intensity regime, the sample experiences severe ionization via x-ray multiphoton multiple ionization dynamics. Thus, it becomes necessary to take into account all the contributions to the Compton scattering signal when atoms are exposed to high-intensity x-ray pulses provided by x-ray free-electron lasers (XFELs). In this paper, we investigate the Compton spectra of atoms at high x-ray intensity, using an extension of the integrated x-ray atomic physics toolkit, \textsc{xatom}. As the x-ray fluence increases, there is a significant contribution from ionized electrons to the Compton spectra, which gives rise to strong deviations from the Compton spectra of neutral atoms. The present study provides not only understanding of the fundamental XFEL--matter interaction but also crucial information for single-particle imaging experiments, where Compton scattering is no longer negligible.Comment: 24 pages, 10 figures. This is an author-created, un-copyedited version of an article accepted for publication in the special issue of "Emerging Leaders" in J. Phys. B: At. Mol. Opt. Phys. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

Abundances in Stars from the Red Giant Branch Tip to the Near the Main Sequence in M71: I. Sample Selection, Observing Strategy and Stellar Parameters

We present the sample for an abundance analysis of 25 members of M71 with luminosities ranging from the red giant branch tip to the upper main sequence. The spectra are of high dispersion and of high precision. We describe the observing strategy and determine the stellar parameters for the sample stars using both broad band colors and fits of H$\alpha$ profiles. The derived stellar parameters agree with those from the Yale$^2$ stellar evolutionary tracks to within 50 -- 100K for a fixed log g, which is within the level of the uncertainties.Comment: Minor changes to conform to version accepted for publication, with several new figures (Paper 1 of a pair