Methods and Applications of Algorithmic Complexity - Info and Reading Options

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Intro -- Contents -- Part I Theory and Methods -- 1 Preliminaries -- 1.1 Computability and the Behavior of Computing Programs -- 1.1.1 Deterministic Turing Machines -- 1.1.2 The Theory of Cellular Automata -- 1.1.3 Elementary Cellular Automata -- 1.1.4 Wolfram's Classification -- 1.2 Chance and Classical Probability Theory -- 1.2.1 Conditional Probability -- 1.2.2 Shannon's Information Theory -- 1.2.3 Noisy-Channel Coding Theorem and Redundancy -- 1.2.4 Bayes' Theorem -- 1.2.5 Data Compression -- 1.2.6 Compressibility of Cellular Automata -- 1.3 Kolmogorov Complexity and Algorithmic Probability -- References -- 2 Enumerating and Simulating Turing Machines -- 2.1 The Complete Enumeration of (s,k) -- 2.2 Graphical Representation of Turing Machines -- 2.3 The Reduced Enumeration -- 2.4 From Reduced to Complete Enumeration -- 2.5 Simulating Turing Machines -- 2.6 Decoding the Enumeration -- 2.7 Detecting Non-halting Machines -- 2.7.1 Machines Without Transitions to the Halting State -- 2.7.2 Detecting Escapees -- 2.7.3 Detecting Cycles -- 2.8 Running Machines and Storing the Output Strings -- 2.8.1 Producing Random Machines -- 2.9 Halting and Runtime Distributions -- 2.9.1 Halting History of (2,2) and (3,2) Turing Machines -- 2.9.2 Returning the Runtime -- 2.9.3 Two-dimensional Turing Machines -- References -- 3 The Coding Theorem Method -- 3.1 The Limits of Statistical Compression Algorithms -- 3.1.1 The Problem of Short Strings -- 3.2 Approximating the Universal Distribution -- 3.3 The Empirical Distribution D -- 3.4 Methodology -- 3.4.1 Numerical Calculation of D(4) -- 3.4.2 Algorithmic Probability Tables -- 3.4.3 Derivation and Calculation of Algorithmic Complexity -- 3.4.4 Runtimes Investigation -- 3.5 Calculating D(5) -- 3.5.1 Setting the Runtime -- 3.6 A Glance at D(5) -- 3.7 Reliability of the Approximation of D(5)

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