Complexity profiles and generic Muchnik reducibility

We study the relative computational complexity of expansions of Cantor and Baire space in terms of generic Muchnik reducibility. We show that no expansion of Cantor space by countably many unary or closed relations can give a generic Muchnik degree strictly between the degree of Cantor space and the degree of Baire space. Similarly, assuming Delta 12-Wadge determinacy we show that no expansion of Baire space by countably many unary or closed relations can give a generic Muchnik degree strictly between the degree of Baire space and the Borel complete degree. On the other hand, we provide a construction of a degree strictly between the degree of Cantor space and the degree of Baire space and also between the degree of Baire space and the Borel complete degree. (c) 2023 Elsevier Inc. All rights reserved.