Degree theory -- Cupping computably enumerable degrees simultaneously -- The relationship between local and global structure in the enumeration degrees -- A directed system of Scott ideals -- Proof Theory -- The non-normal abyss in Kleene's computability theory -- A Constructive Picture of Noetherianity and Well Quasi-Orders -- Computability -- Symmetry for transfinite computability -- All Melodies are Lost -- Recognizability for weak and strong α-ITRMs -- The de Groot dual of represented spaces -- Algorithmic Randomness -- Some Games on Turing Machines and Power from Random Strings -- Inequalities for entropies and dimensions -- Computational Complexity -- Elementarily traceable irrational numbers -- Logic vs topology on regular ω-languages -- Subrecursive Graphs of Representations of Irrational Numbers -- On the complexity of learning programs -- The Weihrauchcomplexity of the supergraph problem -- Extending Wagner's hierarchy to Deterministic Visibly Pushdown Automata -- On guarded extensions of MMSNP -- Turning block-sequential automata networks into smaller parallel networks with isomorphic limit dynamics -- Interactive proofs -- Structural Complexity of Rational Interactive Proofs -- Physical Zero-Knowledge Proof for Ball Sort Puzzle -- Combinatorial approaches -- Graph subshifts -- Improved Complexity Analysis of Quasi-Polynomial Algorithms Solving Parity Games -- An O(√k)-approximation algorithm for minimum power k edge disjoint st-paths.

This book constitutes the refereed proceedings of the 19th International Conference on Unity of Logic and Computation, CiE 2023, held in Batumi, Georgia, during July 24-28, 2023. The 23 full papers and 13 invited papers included in this book were carefully reviewed and selected from 51 submissions. They were organized in topical sections as follows: Degree theory; Proof Theory; Computability; Algorithmic Randomness; Computational Complexity; Interactive proofs; and Combinatorial approaches.