Manfred Droste Boeken

The purpose of this Handbook is to highlight both theory and applications of weighted automata. Weighted finite automata are classical nondeterministic finite automata in which the transitions carry weights. These weights may model, e. g. , the cost involved when executing a transition, the amount of resources or time needed for this, or the probability or reliability of its successful execution. The behavior of weighted finite automata can then be considered as the function (suitably defined) associating with each word the weight of its execution. Clearly, weights can also be added to classical automata with infinite state sets like pushdown automata; this extension constitutes the general concept of weighted automata. To illustrate the diversity of weighted automata, let us consider the following scenarios. Assume that a quantitative system is modeled by a classical automaton in which the transitions carry as weights the amount of resources needed for their execution. Then the amount of resources needed for a path in this weighted automaton is obtained simply as the sum of the weights of its transitions. Given a word, we might be interested in the minimal amount of resources needed for its execution, i. e. , for the successful paths realizing the given word. In this example, we could also replace the “resources” by “profit” and then be interested in the maximal profit realized, correspondingly, by a given word.

This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory. 

Die vom Abriss der Hochstraße „Tausendfüßler“ übrig gebliebene Stahlstütze und das abmontierte Thyssen/Krupp-Logo am Dreischeibenhaus kennzeichnen das Ende der Baugruppe Thyssen-Dreischeibenhaus, „Tausendfüßler“ und Schauspielhaus, die ab den 1960er Jahren auch international als Ensemble moderner Architektur den Aufbruch Düsseldorfs in die Moderne repräsentierte. Mit dem Abriss des „Tausendfüßlers“ wurde die Baugruppe zerstört, die einen für die jüngere Düsseldorfer Stadtgeschichte charakteristischen Zusammenhang von Wirtschaft, Kultur und Verkehr vermittelte. 35.000 Düsseldorfer nahmen am 24. Februar 2013 Abschied vom „Tausendfüßler“ und bewegten sich zum letzten Mal über die Hochstraße, bevor sie abgerissen wurde.