Searching for Applicable Versions of Computable Structures -- On Measure Quantifiers in First-Order Arithmetic -- Pistone Learning Languages with Decidable Hypotheses -- Robust Online Algorithms for Dynamic Choosing Problems -- On the degrees of constructively immune sets -- Fine-Grained Complexity Theory: Conditional Lower Bounds for Computational Geometry -- The Lost Melody Theorem for Infinite Time Blum-Shub-Smale Machines -- Randomising Realizability -- Restrictions of Hindman's Theorem: an overview -- Complexity and Categoricity of Automatic Injection structures -- A tale of optimizing the space taken by de Bruijn graphs -- Formally Computing with the Non-Computable -- Cohen Mapping Monotonic Restrictions in Inductive Inference -- Normal Forms for Semantically Witness-Based Learners in Inductive Inference -- xWalk-preserving transformation of overlapped sequence graphs into blunt sequence graphs with GetBlunted -- On 3SUM-hard problems in the Decision Tree Model -- Monotonic Spectra and TheirGeneralizations -- On false Heine/Borel compactness principles in proof mining -- Placing Green Bridges Optimally, with a Multivariate Analysis -- A Church-Turing thesis for randomness? -- Probabilistic Models of k-mer Frequencies -- Defining Formal Explanation in Classical Logic by Substructural Derivability -- Dedekind Cuts and Long Strings of Zeros in Base Expansions -- On the impact of treewidth in the computational complexity of freezing dynamics -- Towards a Map for Incremental Learning in the Limit from Positive and Negative Information -- On preserving the computational content of mathematical proofs: toy examples for a formalising strategy -- n search of the first-order part of Ramsey's theorem for pairs -- On subrecursive representability of irrational numbers: Contractors and Baire sequences -- xiLearning -- Languages in the Limit from Positive Information with Finitely Many Memory Changes.

This book constitutes the proceedings of the 17th Conference on Computability in Europe, CiE 2021, organized by the University of Ghent in July 2021. Due to COVID-19 pandemic the conference was held virtually. The 48 full papers presented in this volume were carefully reviewed and selected from 50 submissions. CiE promotes the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences, such as physics and biology, as well as related fields, such as philosophy and history of computing. CiE 2021 had as its motto Connecting with Computability, a clear acknowledgement of the connecting and interdisciplinary nature of the conference series which is all the more important in a time where people are more than ever disconnected from one another due to the COVID-19 pandemic.