Logic and theory of algorithms : 4th Conference on Computability in Europe, CiE 2008, Athens, Greece, June 15-20, 2008 : proceedings

• Main Authors: Conference on Computability in Europe (4th : 2008 : Athens, Greece), Beckmann, Arnold, Dimitracopoulos, Costas, Löwe, Benedikt
• Format: eBook Book
• Language: English
• Published: Berlin Springer 2008; Springer Berlin / Heidelberg
• Edition: 1
• Series: Lecture Notes in Computer Science
• Subjects: Algorithms > Congresses; Computable functions; Computable functions > Congresses; Computational intelligence > Congresses; Congresses; Logic, Symbolic and mathematical > Congresses

CiE 2008: Logic and Theory of Algorithms Athens, Greece, June 15-20, 2008 Computability in Europe (CiE) is an informal network of European scientists working on computability theory, including its foundations, technical devel- ment, and applications. Among the aims of the network is to advance our t...

Table of Contents:

• Classical Fractal Dimensions -- Shannon Information Theory -- Effective Fractal Dimensions -- Classical Dimensions of Saturated Sets -- Our Results -- Preliminaries -- The Four Dimensions -- Relative Frequencies of Digits -- Saturated Sets and Maximum Entropy Principle -- Conclusion -- Reachability in Linear Dynamical Systems -- Introduction -- Prerequisites -- Linear Continuous-Time Dynamical Systems -- Polynomials -- Matrices -- Undecidability for Polynomial Dynamical Systems -- Decidability for Linear Dynamical Systems -- To Put the Matrix in Jordan Form -- If the Matrix Is in Jordan Form -- Hybrid Functional Interpretations -- Introduction -- Multi-modal Linear Logic LL^{\omega}_h -- Kreisel and Gödel Modalities -- A Hybrid Functional Interpretation -- Simple Applications to Program Extraction -- Example 1 -- Example 2 -- Example 3 -- Example 4 -- Comparison to Light Dialectica -- The Light Hybrid Interpretation -- Future Work: Extension and Automation -- Automated Decoration of Modalities -- Conclusion -- The Algorithm Concept - Tool for Historiographic Interpretation or Red Herring? -- A Parallel but Preceding Issue -- Seeing Historical Texts through Algorithms -- Algorithmic Analysis -- The Participants' Point of View -- References -- Adversarial Scheduling Analysis of Game-Theoretic Models of Norm Diffusion -- Introduction -- Preliminaries -- Schedulers -- Peyton Young's Model of Norm Diffusion -- Stochastic Stability -- Results -- Main Result: Diffusion of Norms by Contagion -- The Inertia of Diffusion of Norms with Contagion -- Conclusions and Acknowledgments -- A Simple P-Matrix Linear Complementarity Problem for Discounted Games -- Introduction -- Discounted Games -- A P-Matrix LCP for Discounted Games -- An LCP for Discounted Games -- The P-Matrix Property -- Understanding q and M -- Algorithms -- Unique Sink Orientations of Cubes
• Strategy Improvement and the Strategy Valuation USO -- Murty's Least-Index Method -- Further Research -- Implementing Spi Calculus Using Nominal Techniques -- Introduction -- Spi Calculus -- Isabelle/Nominal -- Encoding Spi Calculus in Isabelle/Nominal -- Implementation of Syntax and Semantics -- Implementation of Hedged Bisimulation -- Example: ``Perfect Encryption'' -- Conclusions and Future Work -- An Enhanced Theory of Infinite Time Register Machines -- Introduction -- Infinite Time Register Machines -- Computing \Pi^1_1-Sets -- ITRMs, ITTMs, and Halting Problems -- Many Facets of Complexity in Logic -- Introduction -- The Computational Complexity Setting -- Finite Model Theory and Descriptive Complexity -- Logics between First-Order and Existential Second-Order -- Bounded Arithmetic -- The Language and Translation from the Finite Model Theory Setting -- Systems of Bounded Arithmetic -- Defining Functions in the Bounded Arithmetic Setting -- When Do Systems Based on Formulas Describing a Complexity Class Capture the Same Class? -- Conclusions -- On the Computational Power of Enhanced Mobile Membranes -- Introduction -- Systems with Enhanced Mobile Membranes -- Computational Power -- Conclusion -- Recursion in Higher Types and Resource Bounded Turing Machines -- Introduction -- A Brief Discussion -- Computability and Complexity in Self-assembly -- Introduction -- Preliminaries -- Pseudoseeds and Multiseeds -- Self-assembly of Computably Enumerable Sets -- Overview of Construction -- The Ray Module -- The Planter Module -- The Computation Module -- Sketch of Correctness Proof -- A Decidable Set That Does Not Self-assemble -- Conclusion -- Extraction in Coq: An Overview -- Introduction -- Extraction in Practice : Div -- A Division That Fulfills the Structural Constraint -- A Division with an Explicit Counter
• Title Page -- Preface -- Table of Contents -- Deterministic Graphical Games Revisited -- Introduction -- Simple Stochastic Games -- Deterministic Graphical Games -- Our Results -- Preliminaries -- Solving Deterministic Graphical Games -- Strongly -- Weakly -- Program Schemes with Deep Pushdown Storage -- Introduction -- Basic Definitions -- Our Results -- Restricted Program Schemes -- Capturing NP -- Beyond NP -- Capturing PSPACE -- Beyond PSPACE -- Conclusions -- Herbrand Theorems and Skolemization for Prenex Fuzzy Logics -- Introduction -- Fuzzy Logics -- Herbrand Theorems -- Approximate Herbrand Theorems -- Skolemization -- Decidability of Hybrid Logic with Local Common Knowledge Based on Linear Temporal Logic LTL -- Introduction -- Preliminaries, Definitions, Notation -- Decidability Algorithm for LTL_ACK -- Conclusion, Future Work -- Pure Iteration and Periodicity -- Introduction and Notation -- Background and Motivation -- The Hierarchy IT -- A Note on Presburger Arithmetic and IT -- Discussion and Directions for Further Research -- Programming Experimental Procedures for Newtonian Kinematic Machines -- Introduction -- Experimental Procedures and Languages -- Experimental Procedures and Pseudocode -- A Simple Language EP(T) for Experimental Procedures -- Behaviour of Procedures -- Examples -- Routines -- Restrictions and Extensions of the Language for Experimental Procedures -- Physical Extensions -- Mathematical Extensions -- Experimental Computation with Rational Numbers -- Concluding Remarks -- Linear, Polynomial or Exponential? Complexity Inference in Polynomial Time -- Introduction -- Problem Definition -- A Calculus to Certify Polynomial Bounds -- Data Flow Relations -- Certifying Linear Bounds -- Analysing Running Time -- Concluding Remarks -- A Summation Algorithm from 11th Century China -- Shen Gua's Text
• A Week-End Off: The First Extensive Number-Theoretical Computation on the ENIAC -- Introduction -- How a Number-Theorist Got Involved with Computers -- The Structure of the ENIAC -- Lehmer's ENIAC `Program' -- The Mathematical Problem -- Description of the Main Steps of the Computation -- Outline of the Set-Up of the Computation on the ENIAC -- Discussion -- Phase Transitions for Weakly Increasing Sequences -- Introduction -- Classifying Phase Transitions for Weakly Increasing Sequences -- The Erdös-Szekeres Theorem and the Dilworth Decomposition Theorem -- Succinct NP Proofs from an Extractability Assumption -- Introduction -- Definitions and Tools -- An Extractability Assumption -- Our EA Assumption -- A Low-Communication 1-Round Argument for NP -- Describing the Wadge Hierarchy for the Alternation Free Fragment of μ-Calculus (I) -- Introduction -- The Propositional Modal \mu-Calculus -- Syntax and Semantics -- The Alternation Free Fragment -- Evaluation Game for the \mu-Calculus -- The Wadge Hierarchy -- Main Result -- Conclusion -- Subrecursive Complexity of Identifying the Ramsey Structure of Posets -- Introduction -- Preliminaries -- Layered Posets -- The First Amalgamation -- The Second Amalgamation -- Solving Simple Stochastic Games -- Introduction -- References -- The Shrinking Property for NP and coNP -- Introduction -- Preliminaries -- Disjoint NP-Pairs -- Function Classes -- Connections to Reasonable Assumptions -- Oracle Separations -- Conclusions and Open Questions -- On the Hardness of Truthful Online Auctions with Multidimensional Constraints -- Introduction and Related Work -- Previous Work -- Our Results -- Model and Definitions -- First Impossibility: With Private Time Parameters -- Second Impossibility: Relaxing Private Time Parameters -- Conclusions -- Effective Dimensions and Relative Frequencies -- Introduction
• Shen Gua's Algorithm -- Conclusion -- Sequential Automatic Algebras -- General Properties, Separating Examples and Classification Results -- Linear Order Algebras -- Sequential Automatic Unary Algebras -- The Role of Classical Computation in Measurement-Based Quantum Computation -- Introduction -- One-Way Model of Quantum Computation -- CNOT Computers -- Discussion -- The Algebraic Counterpart of the Wagner Hierarchy -- Introduction -- Preliminaries -- \omega-Languages -- \omega-Semigroups -- The Wadge and the Wagner Hierarchies -- The \mathbb{SG}-Hierarchy -- The \mathbb{FSG} and the Wagner Hierarchies -- Conclusion -- Computing by Observing: A Brief Survey -- Introduction -- Computing by Observing -- An Example of Observer: Automata with Singular Output -- G/O Systems -- Always Writing G/O Systems -- Initial G/O Systems -- Free G/O Systems -- Computing by Only Observing -- Restrictions on the Observed System -- Final Remarks -- A Quantum Information-Theoretic Proof of the Relation between Horn's Problem and the Littlewood-Richardson Coefficients -- Introduction and Results -- Preliminaries -- Spectrum Estimation -- Littlewood-Richardson Coefficients -- Proofs -- From Hermitian Operators to Density Operators -- Proof of Theorem 5 -- Proof of Theorem 6 -- Pell Equations and Weak Regularity Principles -- Introduction -- Limit Schemata and Weak Regularity -- Dirichlet's Approximation Lemma in IE_1 -- Bounded WR vs. exp -- Computable Categoricity of Graphs with Finite Components -- Introduction -- Computable Categoricity and the Size Function -- A Sufficient Condition for Not Computably Categorical -- Infinite Chains of Embedded Components -- P Automata: Membrane Systems as Acceptors -- On the Processing Power of Protozoa -- Computing Equilibria in Large Games We Play
• A Division by General Recursion, Historical Approach