Bounds on the Automata Size for Presburger Arithmetic

Automata provide a decision procedure for Presburger arithmetic. However, until now only crude lower and upper bounds were known on the sizes of the automata produced by this approach. In this paper, we prove an upper bound on the the number of states of the minimal deterministic automaton for a Presburger arithmetic formula. This bound depends on the length of the formula and the quantifiers occurring in the formula. The upper bound is established by comparing the automata for Presburger arithmetic formulas with the formulas produced by a quantifier elimination method. We also show that our bound is tight, even for nondeterministic automata. Moreover, we provide optimal automata constructions for linear equations and inequations

The \mu-Calculus Alternation Hierarchy Collapses over Structures with Restricted Connectivity

It is known that the alternation hierarchy of least and greatest fixpoint operators in the mu-calculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of structures. A prominent instance is the class of infinite words over which the alternation-free fragment is already as expressive as the full mu-calculus. Our current understanding of when and why the mu-calculus alternation hierarchy is not strict is limited. This paper makes progress in answering these questions by showing that the alternation hierarchy of the mu-calculus collapses to the alternation-free fragment over some classes of structures, including infinite nested words and finite graphs with feedback vertex sets of a bounded size. Common to these classes is that the connectivity between the components in a structure from such a class is restricted in the sense that the removal of certain vertices from the structure's graph decomposes it into graphs in which all paths are of finite length. Our collapse results are obtained in an automata-theoretic setting. They subsume, generalize, and strengthen several prior results on the expressivity of the mu-calculus over restricted classes of structures.Comment: In Proceedings GandALF 2012, arXiv:1210.202

Don't care words with an application totheautomata-based approach for real addition

Automata have proved to be a useful tool in infinite-state model checking, since they can represent infinite sets of integers and reals. However, analogous to the use of binary decision diagrams (bdds) to represent finite sets, the sizes of the automata are an obstacle in the automata-based set representation. In this article, we generalize the notion of "don't cares” for bdds to word languages as a means to reduce the automata sizes. We show that the minimal weak deterministic Büchi automaton (wdba) with respect to a given don't care set, under certain restrictions, is uniquely determined and can be efficiently constructed. We apply don't cares to improve the efficiency of a decision procedure for the first-order logic over the mixed linear arithmetic over the integers and the reals based on wdba

Ertrag und Qualitätsparameter von Winterweizensorten aus biologischer und konventioneller Züchtung in Luxemburg

Thirteen winter wheat varieties (Triticum aestivum L.) bred in conventional breeding programs and seven varieties from organic breeding were tested under organic conditions in two locations in 2009/10 and 2010/11 in Luxembourg. The objective was to analyze whether these conditions, organic varieties perform better than conventional ones. Grain yield (dt ha-1), protein content (%) and Zeleny sedimentation value were analyzed. The effect of the factor variety was statistically significant at a probability level of 0.05 for the three traits. For grain yield, the variety x year x location interaction was significant. For protein content, the variety x year interaction was significant. Location x year interaction was significant for sedimentation value. Results indicate that organic varieties generally lead to lower grain yields with higher baking quality (protein content and sedimentation value) than conventional varieties. However, a large range of grain yields, protein contents and sedimentation values were observed for both categories

Runtime Monitoring of Metric First-order Temporal Properties

We introduce a novel approach to the runtime monitoring of complex system properties. In particular, we present an online algorithm for a safety fragment of metric first-order temporal logic that is considerably more expressive than the logics supported by prior monitoring methods. Our approach, based on automatic structures, allows the unrestricted use of negation, universal and existential quantification over infinite domains, and the arbitrary nesting of both past and bounded future operators. Moreover, we show how to optimize our approach for the common case where structures consist of only finite relations, over possibly infinite domains. Under an additional restriction, we prove that the space consumed by our monitor is polynomially bounded by the cardinality of the data appearing in the processed prefix of the temporal structure being monitored

On regular temporal logics with past

The IEEE standardized Property Specification Language, PSL for short, extends the well-known linear-time temporal logic LTL with so-called semi-extended regular expressions. PSL and the closely related SystemVerilog Assertions, SVA for short, are increasingly used in many phases of the hardware design cycle, from specification to verification. In this article, we extend the common core of these specification languages with past operators. We name this extension PPSL. Although all ω-regular properties are expressible in PSL, SVA, and PPSL, past operators often allow one to specify properties more naturally and concisely. In fact, we show that PPSL is exponentially more succinct than the cores of PSL and SVA. On the star-free properties, PPSL is double exponentially more succinct than LTL. Furthermore, we present a translation of PPSL into language-equivalent nondeterministic Büchi automata, which is based on novel constructions for 2-way alternating automata. The upper bound on the size of the resulting nondeterministic Büchi automata obtained by our translation is almost the same as the upper bound for the nondeterministic Büchi automata obtained from existing translations for PSL and SVA. Consequently, the satisfiability problem and the model-checking problem for PPSL fall into the same complexity classes as the corresponding problems for PSL and SV

Overcoming losses with gain in a negative refractive index metamaterial

On the basis of a full-vectorial three-dimensional Maxwell-Bloch approach we investigate the possibility of using gain to overcome losses in a negative refractive index fishnet metamaterial. We show that appropriate placing of optically pumped laser dyes (gain) into the metamaterial structure results in a frequency band where the nonbianisotropic metamaterial becomes amplifying. In that region both the real and the imaginary part of the effective refractive index become simultaneously negative and the figure of merit diverges at two distinct frequency points.Comment: 4 pages, 4 figure

Erste Ergebnisse eines Artenvergleichs von Erbsen und Ackerbohnen

Organic farmers have to take the decision which grain legume specie is the best for their site. The existing recommendations are based on variety tests and studies on cropping systems. The best grain leg¬ume specie on one site has not been investigated. The aim of this work is to test field pea and faba bean on one and the same site. In 2011/2012 these two species were sown in autumn and in spring, as well as in pure stand and in mixture with cereals (for the field pea) in a field trial. Hardiness of the winter crops and yield were assessed. Winter field pea in mixture with triticale had the highest hardiness and was significantly different from field pea in pure stand and from faba bean. Spring faba bean was the crop with the highest yield and had no significant difference from the winter form and the spring field pea. Results show that it is important to test different grain legume species on one and the same site

Organic seed health. An inventory of issues and a report on case studies.

This report describes the state of the art and research results on the production of heathy organic seeds, as performed in the frame of the LIVESEED project, with support from the European Horizon 2020 program. Organic seed health is based on a multitude of factors and cannot simply be managed through one-size-fits-all solutions such as curative seed treatments. Use of seeds produced under organic conditions can also have benefits, as organic soils may have a richer and more diverse microbiome and part of this microbiome enters the seed during development. Although much more research is needed, there are indications that certain microorganisms in this seed microbiome play a role in tolerance of the emerging seedling toward biotic and abiotic stress in the field. In the frame of the LIVESEED project, case studies have been performed on some of these issues, with the aim of providing background information and tools to tackle them