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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