This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, June/July 2006. The book presents 31 revised full papers together with 30 invited papers, including papers corresponding to 8 plenary talks and 6 special sessions on proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and Gödel centenary: Gödel's legacy for computability.
Heap-Abstraction for an Object-Oriented Calculus with Thread Classes.- From Constructibility and Absoluteness to Computability and Domain Independence.- Datatype-Generic Reasoning.- The Logical Strength of the Uniform Continuity Theorem.- Elementary Algebraic Specifications of the Rational Function Field.- Random Closed Sets.- Deep Inference and Its Normal Form of Derivations.- Logspace Complexity of Functions and Structures.- Prefix-Like Complexities and Computability in the Limit.- Partial Continuous Functions and Admissible Domain Representations.- An Invariant Cost Model for the Lambda Calculus.- On the Complexity of the Sperner Lemma.- The Church-Turing Thesis: Consensus and Opposition.- Gödel and the Origins of Computer Science.- The Role of Algebraic Models and Type-2 Theory of Effectivity in Special Purpose Processor Design.- Turing Universality in Dynamical Systems.- Every Sequence Is Decompressible from a Random One.- Reversible Conservative Rational Abstract Geometrical Computation Is Turing-Universal.- LJQ: A Strongly Focused Calculus for Intuitionistic Logic.- Böhm Trees, Krivine’s Machine and the Taylor Expansion of Lambda-Terms.- What Does the Incompleteness Theorem Add to the Unsolvability of the Halting Problem?.- An Analysis of the Lemmas of Urysohn and Urysohn-Tietze According to Effective Borel Measurability.- Enumeration Reducibility with Polynomial Time Bounds.- Coinductive Proofs for Basic Real Computation.- A Measure of Space for Computing over the Reals.- On Graph Isomorphism for Restricted Graph Classes.- Infinite Time Register Machines.- Upper and Lower Bounds on Sizes of Finite Bisimulations of Pfaffian Hybrid Systems.- Forcing with Random Variables and Proof Complexity.- Complexity-Theoretic Hierarchies.- Undecidability in the Homomorphic Quasiorder of Finite Labeled Forests.- Lower Bounds Using Kolmogorov Complexity.- The Jump Classes of Minimal Covers.- Space Bounds for Infinitary Computation.- From a Zoo to a Zoology: Descriptive Complexity for Graph Polynomials.- Towards a Trichotomy for Quantified H-Coloring.- Two Open Problems on Effective Dimension.- Optimization and Approximation Problems Related to Polynomial System Solving.- Uncomputability Below the Real Halting Problem.- Constraints on Hypercomputation.- Martingale Families and Dimension in P.- Can General Relativistic Computers Break the Turing Barrier?.- Degrees of Weakly Computable Reals.- Understanding and Using Spector’s Bar Recursive Interpretation of Classical Analysis.- A Subrecursive Refinement of the Fundamental Theorem of Algebra.- An Introduction to Program and Thread Algebra.- Fast Quantifier Elimination Means P = NP.- Admissible Representations in Computable Analysis.- Do Noetherian Modules Have Noetherian Basis Functions?.- Inverting Monotone Continuous Functions in Constructive Analysis.- Partial Recursive Functions in Martin-Löf Type Theory.- Partially Ordered Connectives and ?1 1 on Finite Models.- Upper and Lower Bounds for the Computational Power of P Systems with Mobile Membranes.- Gödel’s Conflicting Approaches to Effective Calculability.- Co-total Enumeration Degrees.- Relativized Degree Spectra.- Phase Transition Thresholds for Some Natural Subclasses of the Computable Functions.- Non-deterministic Halting Times for Hamkins-Kidder Turing Machines.- Kurt Gödel and Computability Theory.- A Computability Theory of Real Numbers.- Primitive Recursive Selection Functions over Abstract Algebras.
