Equivalence of Deterministic One-Counter Automata is NL-complete

We prove that language equivalence of deterministic one-counter automata is NL-complete. This improves the superpolynomial time complexity upper bound shown by Valiant and Paterson in 1975. Our main contribution is to prove that two deterministic one-counter automata are inequivalent if and only if they can be distinguished by a word of length polynomial in the size of the two input automata

Orbital frequencies in the carbonate sedimentary record: distorted by diagenesis?

The most important archive of Earth’s climate change through geologic history is the sedimentary rock record. Rhythmic sedimentary alternations are usually interpreted as a consequence of periodic variations in the orbital parameters of the Earth. This interpretation enables the application of cyclostratigraphy as a very precise chronometer, when based on the assumption that orbital frequencies are faithfully recorded in the sedimentary archive. However, there are numerous uncertainties with the application of this concept. Particularly in carbonates, sediment properties such as mineralogical composition and fossil associations are severely altered during post-depositional alteration (diagenesis). We here point out that the assumption of a 1:1 recording of orbital signals in many cases is questionable for carbonate rhythmites. We use computer simulations to show the effect of diagenetic overprint on records of orbital signals in the carbonate record. Such orbital signals may be distorted in terms of frequency, amplitude, and phase by diagenetic processes, and cycles not present in the insolation record may emerge. This questions the routine use of carbonate rhythmites for chronostratigraphic datin

Bayesian weak lensing tomography: Reconstructing the 3D large-scale distribution of matter with a lognormal prior

We present a Bayesian reconstruction algorithm that infers the three-dimensional large-scale matter distribution from the weak gravitational lensing effects measured in the image shapes of galaxies. The algorithm is designed to also work with non-Gaussian posterior distributions which arise, for example, from a non-Gaussian prior distribution. In this work, we use a lognormal prior and compare the reconstruction results to a Gaussian prior in a suite of increasingly realistic tests on mock data. We find that in cases of high noise levels (i.e. for low source galaxy densities and/or high shape measurement uncertainties), both normal and lognormal priors lead to reconstructions of comparable quality, but with the lognormal reconstruction being prone to mass-sheet degeneracy. In the low-noise regime and on small scales, the lognormal model produces better reconstructions than the normal model: The lognormal model 1) enforces non-negative densities, while negative densities are present when a normal prior is employed, 2) better traces the extremal values and the skewness of the true underlying distribution, and 3) yields a higher pixel-wise correlation between the reconstruction and the true density.Comment: 23 pages, 12 figures; updated to match version accepted for publication in PR

A Database on Musicians’ Movements During Musical Performances

The movements of 20 musicians playing 11 different musical instruments, including all standard orchestral instruments, were captured during solo performances by means of a motion capturing system under concert-like conditions.DFG, FOR 1557, Simulation and Evaluation of Acoustical Environments (SEACEN

Bisimulation equivalence and regularity for real-time one-counter automata

A one-counter automaton is a pushdown automaton with a singleton stack alphabet, where stack emptiness can be tested; it is a real-time automaton if it contains no ε -transitions. We study the computational complexity of the problems of equivalence and regularity (i.e. semantic finiteness) on real-time one-counter automata. The first main result shows PSPACEPSPACE-completeness of bisimulation equivalence; this closes the complexity gap between decidability [23] and PSPACEPSPACE-hardness [25]. The second main result shows NLNL-completeness of language equivalence of deterministic real-time one-counter automata; this improves the known PSPACEPSPACE upper bound (indirectly shown by Valiant and Paterson [27]). Finally we prove PP-completeness of the problem if a given one-counter automaton is bisimulation equivalent to a finite system, and NLNL-completeness of the problem if the language accepted by a given deterministic real-time one-counter automaton is regular.Web of Science80474372