Dagstuhl-Seminar — Weihrauch Complexity: Structuring the Realm of Non-Computability

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.