Mathematical Theory and Computational Practice

This book constitutes the proceedings of the 5th Conference on Computability in Europe, CiE 2009, held in Heidelberg, Germany, during July 19-24, 2009.

The 34 papers presented together with 17 invited lectures were carefully reviewed and selected from 100 submissions. The aims of the conference is to advance our theoretical understanding of what can and cannot be computed, by any means of computation. It is the largest international meeting focused on computability theoretic issues.

Inhalt

First-Order Universality for Real Programs.- Skolem + Tetration Is Well-Ordered.- Structures of Some Strong Reducibilities.- Complexity of Existential Positive First-Order Logic.- Stochastic Programs and Hybrid Automata for (Biological) Modeling.- Numberings and Randomness.- The Strength of the Grätzer-Schmidt Theorem.- Hyperloops Do Not Threaten the Notion of an Effective Procedure.- Minimum Entropy Combinatorial Optimization Problems.- Program Self-reference in Constructive Scott Subdomains.- and Equivalence Structures.- Immunity for Closed Sets.- Lower Bounds for Kernelizations and Other Preprocessing Procedures.- Infinite-Time Turing Machines and Borel Reducibility.- Cutting Planes and the Parameter Cutwidth.- Members of Random Closed Sets.- Lowness for Demuth Randomness.- Graph States and the Necessity of Euler Decomposition.- On Stateless Multicounter Machines.- Computability of Continuous Solutions of Higher-Type Equations.- Equivalence Relations on Classes of Computable Structures.- Fractals Generated by Algorithmically Random Brownian Motion.- Computable Exchangeable Sequences Have Computable de Finetti Measures.- Spectra of Algebraic Fields and Subfields.- Definability in the Local Theory of the ?-Enumeration Degrees.- Computability of Analytic Functions with Analytic Machines.- An Application of Martin-Löf Randomness to Effective Probability Theory.- Index Sets and Universal Numberings.- Ordinal Computability.- A Gandy Theorem for Abstract Structures and Applications to First-Order Definability.- Constructing New Aperiodic Self-simulating Tile Sets.- Relationship between Kanamori-McAloon Principle and Paris-Harrington Theorem.- The First Order Theories of the Medvedev and Muchnik Lattices.- Infima of d.r.e. Degrees.- A Divergence Formula forRandomness and Dimension.- On Ladner's Result for a Class of Real Machines with Restricted Use of Constants.- 0?-Categorical Completely Decomposable Torsion-Free Abelian Groups.- Notes on the Jump of a Structure.- A General Representation Theorem for Probability Functions Satisfying Spectrum Exchangeability.- Stability under Strategy Switching.- Computational Heuristics for Simplifying a Biological Model.- Functions Definable by Arithmetic Circuits.- Survey on Oblivious Routing Strategies.- An Approach to the Engineering of Cellular Models Based on P Systems.- Decidability of Sub-theories of Polynomials over a Finite Field.- Chaitin ? Numbers and Halting Problems.- Bayesian Data Integration and Enrichment Analysis for Predicting Gene Function in Malaria.- Dialectica Interpretation with Fine Computational Control.- Algorithmic Minimal Sufficient Statistic Revisited.- A Computation of the Maximal Order Type of the Term Ordering on Finite Multisets.- On Generating Independent Random Strings.