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Hausdorff Research Institute for Mathematics (HIM)

The trimester program aims to bring together experts, postdocs, and students in computer science and certain areas in mathematics (analysis, probability, and combinatorics) in order to learn about some challenging open problems recently raised in computer science, to use and invent necessary new tools and techniques in mathematics to solve these challenging problems, and vice versa to learn and further extend methods developed in computer science to develop new directions in mathematics motivated by questions in computer science. The core topics of the trimester program would be: learning theory, complexity of classical and quantum algorithms, vector valued functions on the hypercube, complex Hypercontractivity, polynomial inequalities on the hypercube, and discrete approximation theory on the hamming cube.

Analysis,    Kurse und Veranstaltungen für Studenten der Mathematik

The Hausdorff Research Institute for Mathematics (HIM)

This workshop brings together leading experts in Boolean analysis, information theory, and lattices to explore the forefront of these disciplines through the talks and discussions about intriguing open problems, recent resolutions, and the evolution of innovative ideas, approaches, and techniques.

Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH

Logic and learning are central to Computer Science, and in particular to AI-related research. Already Alan Turing envisioned in his 1950 “Computing Machinery and Intelligence” paper a combination of statistical (ab initio) machine learning and an “unemotional” symbolic language such as logic. The combination of logic and learning has received new impetus from the spectacular success of deep learning systems. The goal of this Dagstuhl Seminar is to bring together researchers from various communities related to utilizing logical constraints in deep learning and to create bridges between them via the exchange of ideas.

Neuronale Netze und Künstliche Intelligenz, Maschinelles Lernen,    Implementierung und Anwendungen von künstlicher Intelligenz

Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH

Semirings are fundamental algebraic structures that in recent times have found a number of applications to computer science, especially in the areas of databases and automata. On the side of databases, commercial query languages, such as SQL, use bag semantics, instead of set semantics, to evaluate relational database queries, which means that the semiring of the natural numbers is used to annotate tuples in the input and output relations. More generally, the annotations can be values in some fixed semiring; this gives a common generalization of both set semantics and bag semantics of database queries, and also makes it possible to model other situations in which one is interested, e.g., in the probability or the reliability of an answer. Furthermore, semirings of polynomials have been successfully used to carry out a rigorous study of provenance in databases. On the side of automata, semirings are used to define weighted automata, which are nondeterministic finite automata augmented with values from a semiring as weights on the transitions. 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. Weighted automata have found numerous applications to natural language processing, speech recognition, and algorithms for digital image compression. These applications have inspired numerous investigations in the logic-in-computer-science community.

Softwareentwicklung,    Datenbanktechlologie, Suchmaschinen und Data-Mining

Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH

This Dagstuhl Seminar is dedicated to the investigation of two active areas of research, one in theoretical computer science, the other in mathematical logic. These are computable analysis on the one hand, and reverse mathematics and applied computability theory on the other. That there is a deep connection between these areas was first suggested by Gherardi and Marcone (2008) and later independently by Dorais, Dzhafarov, Hirst, Mileti, and Shafer (2016) and Hirschfeldt and Jockusch (2016). The past decade has seen this connection blossom into a rich and productive area of research, with by now many papers and several PhD theses dedicated to it. Results in this area fall into two intertwined groups: Some clarify the structure of the degrees of non-computability; some further our understanding of the precise nature of non-computability of particular computational tasks of interest. Grasping the nature of non-computability is a profound goal mirroring the quest to understand the nature of computation. Knowing the degree of non-computability of a computational task brings with it answers as to whether weaker or approximate versions of it might be solvable. This interdisciplinary development was fostered not least by the two precursor Dagstuhl Seminars on this topic. The current seminar will explore recent trends and results, open questions, and new directions of this fascinating field of research that has become known as Weihrauch complexity.

Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH

Categorical methods have a long history in automata and language theory, but a coherent theory has started to emerge only in recent years. Some recent examples of categorical methods in automata theory include monadic, coalgebraic, functorial, fibrational and profinite approaches. Such an abstract viewpoint can provide a unifying perspective on various forms of automata; it can make it easier to bootstrap a theory in a new setting; and it provides conceptual clarity regarding which aspects and properties are fundamental and which are only coincidental. Due to being in its early stages, the field is currently still divided into several different communities with little connections between them. The purpose of this seminar is to connect these communities; to initiate collaborations; and to discuss recent developments and possible ways to go forward. The seminar will mix researchers of different backgrounds, in order to achieve a healthy balance between abstraction and applications in automata theory. We hope that the meeting will foster further interaction between the different communities. It should benefit category theorists, who may or may not have studied computation theory before, by inspiring them to look at problems motivated by automata and formal languages

Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH

The main aim of this Dagstuhl Seminar is to bring together leading researchers from all areas of activity in the theory of computation who use the constraint satisfaction paradigm, so that they can communicate state-of-the-art advances, share deep insights, and embark on a systematic interaction that will further develop the synergy between the different areas, generate new research avenues, and lead to fruitful attacks on the open problems in this area.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Graphentheorie und Kombinatorik,    Statistik, Spieltheorie