How Much Lookahead is Needed to Win Infinite Games?

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. For $\omega$-regular winning conditions it is known that such games can be solved in doubly-exponential time and that doubly-exponential lookahead is sufficient. We improve upon both results by giving an exponential time algorithm and an exponential upper bound on the necessary lookahead. This is complemented by showing EXPTIME-hardness of the solution problem and tight exponential lower bounds on the lookahead. Both lower bounds already hold for safety conditions. Furthermore, solving delay games with reachability conditions is shown to be PSPACE-complete. This is a corrected version of the paper https://arxiv.org/abs/1412.3701v4 published originally on August 26, 2016

Prompt Delay

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. Recently, such games with quantitative winning conditions in weak MSO with the unbounding quantifier were studied, but their properties turned out to be unsatisfactory. In particular, unbounded lookahead is in general necessary. Here, we study delay games with winning conditions given by Prompt-LTL, Linear Temporal Logic equipped with a parameterized eventually operator whose scope is bounded. Our main result shows that solving Prompt-LTL delay games is complete for triply-exponential time. Furthermore, we give tight triply-exponential bounds on the necessary lookahead and on the scope of the parameterized eventually operator. Thus, we identify Prompt-LTL as the first known class of well-behaved quantitative winning conditions for delay games. Finally, we show that applying our techniques to delay games with \omega-regular winning conditions answers open questions in the cases where the winning conditions are given by non-deterministic, universal, or alternating automata

Otto Hesse / in moderner Rechtschreibung neu hrsg. von Gabriele Dörflinger, Universitätsbibliothek Heidelberg

Otto Hesse (1811-1874) studierte Mathematik an der Universität Königsberg und lehrte dort bis 1855. Im April 1856 wurde er als ordentl. Professor an die Universität Heidelberg berufen. Er arbeitete über Geometrie und Algebra. 1868 folgte er einen Ruf an die neue Technische Hochschule in München. Der Originalaufsatz wurde in der vor 1900 gültigen Rechtschreibung publiziert. Die Neuausgabe benutzt die aktuelle Rechtschreibung

Riemann und seine Bedeutung für die Entwickelung der modernen Mathematik / neu hrsg. von Gabriele Dörflinger

Felix Klein (1849-1925) würdigt in seinem Eröffnungsvortrag der Versammlung der Deutschen Mathematiker-Vereinigung 1894 in Wien vor allem Bernhard Riemanns bahnbrechende Leistungen auf dem Gebiet der komplexen Funktionen und der Potenzialtheorie. Er schildert auch Riemanns Beiträge zur Theorie der Differentialgleichungen, zu den trigonometrischen Reihen und zu den Grundlagen der Geometrie

Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert : ausgewählte Passagen bezüglich Heidelberger Mathematiker / zusammengestellt von Gabriele Dörflinger

Bericht über wichtige Erfoschungsergebnisse der Mathematik im 19. Jahundert, an denen folgende mit Heidelberg verbundene Personen beteiligt waren: August Leopold Crelle, Julius Plücker, Jakob Steiner, Otto Hesse, Gustav R. Kirchhoff, Hermann Helmholtz, Sonja Kowalevsky [Sof'ja V. Kovalevskaja], Heinrich Weber, Georg Landsberg und David Hilbert

Synthesizing Functional Reactive Programs

Functional Reactive Programming (FRP) is a paradigm that has simplified the construction of reactive programs. There are many libraries that implement incarnations of FRP, using abstractions such as Applicative, Monads, and Arrows. However, finding a good control flow, that correctly manages state and switches behaviors at the right times, still poses a major challenge to developers. An attractive alternative is specifying the behavior instead of programming it, as made possible by the recently developed logic: Temporal Stream Logic (TSL). However, it has not been explored so far how Control Flow Models (CFMs), as synthesized from TSL specifications, can be turned into executable code that is compatible with libraries building on FRP. We bridge this gap, by showing that CFMs are indeed a suitable formalism to be turned into Applicative, Monadic, and Arrowized FRP. We demonstrate the effectiveness of our translations on a real-world kitchen timer application, which we translate to a desktop application using the Arrowized FRP library Yampa, a web application using the Monadic threepenny-gui library, and to hardware using the Applicative hardware description language ClaSH.Comment: arXiv admin note: text overlap with arXiv:1712.0024

How companies succeed in developing ethical artificial intelligence (AI)

The rapid advancement of artificial intelligence (AI) has the potential to bring great benefits to society, but also raises important ethical and moral questions. To ensure that AI systems are developed and deployed in a responsible and ethical manner, companies must consider a number of factors, including fairness, accountability, transparency, privacy, and consistency with human values. This essay provides an overview of the key considerations for building an ethical AI system and briefly discusses the challenges, including the importance of developing AI systems with a clear understanding of their potential impact on society and taking steps to mitigate any potential negative consequences. This essay also highlights the need for continuous monitoring and evaluation of AI systems and outlines a strategy, namely an enterprise-wide "Ethics Sheet for AI tasks", to ensure that AI systems are used in an ethical and responsible manner within the company. Ultimately, building an ethical AI system requires a commitment to transparency, accountability, and a clear understanding of the ethical and moral implications of AI technology, and the company must be aware of the long-term consequences of using a non-ethical and morally questionable AI system. (DIPF/Orig.