Avoiding Simplicity Is Complex -- Higher-Order Containers -- On the Completeness of Quantum Computation Models -- The Ordinal of Skolem + Tetration Is ? 0 -- Proofs, Programs, Processes -- Ergodic-Type Characterizations of Algorithmic Randomness -- How Powerful Are Integer-Valued Martingales? -- A Faster Algorithm for Finding Minimum Tucker Submatrices -- Processes in Space -- Computability of Countable Subshifts -- The Limits of Tractability in Resolution-Based Propositional Proof Systems -- Haskell before Haskell: Curry’s Contribution to Programming (1946–1950) -- A Miniaturisation of Ramsey’s Theorem -- Graph Structures and Algorithms for Query-Log Analysis -- On the Complexity of Local Search for Weighted Standard Set Problems -- Computational Interpretations of Analysis via Products of Selection Functions -- The Peirce Translation and the Double Negation Shift -- Counting the Changes of Random Sets -- Boole: From Calculating Numbers to Calculating Thoughts -- Approximability and Hardness in Multi-objective Optimization -- Is Not a Heyting Algebra -- Lower Bounds for Reducibility to the Kolmogorov Random Strings -- Spatial Models for Virtual Networks -- DNA Rearrangements through Spatial Graphs -- On Index Sets of Some Properties of Computable Algebras -- The Strength of the Besicovitch-Davies Theorem -- Circuit Complexity and Multiplicative Complexity of Boolean Functions -- Definability in the Subword Order -- Undecidability in Weihrauch Degrees -- Degrees with Almost Universal Cupping Property -- Incomputability in Physics -- Approximate Self-assembly of the Sierpinski Triangle -- Hairpin Lengthening -- Infinities in Quantum Field Theory and in Classical Computing: Renormalization Program -- Computational Complexity Aspects in Membrane Computing -- Computable Ordered Abelian Groups and Fields -- Focusing in Asynchronous Games -- A Note on the Least Informative Model of a Theory -- Three Roots for Leibniz’s Contribution to the Computational Conception of Reason -- Development of a Bacteria Computer: From in silico Finite Automata to in vitro and in vivo -- The Complexity of Explicit Constructions -- Kolmogorov Complexity Cores -- Every -Set Is Natural, Up to Turing Equivalence -- Computable Fields and Weak Truth-Table Reducibility -- What Is the Problem with Proof Nets for Classical Logic? -- Quasi-linear Dialectica Extraction -- Computing with Concepts, Computing with Numbers: Llull, Leibniz, and Boole -- Inference Concerning Physical Systems.

This book constitutes the refereed proceedings of the 6th Conference on Computability in Europe, CiE 2010, held in Ponta Delgada, Azores, Portugal, in June/July 2010. The 28 revised papers presented together with 20 invited lectures were carefully reviewed and selected from 90 submissions. The papers address not only the more established lines of research of computational complexity and the interplay between proofs and computation, but also novel views that rely on physical and biological processes and models to find new ways of tackling computations and improving their efficiency.