This review volume consists of a set of chapters written by leading scholars, most of them founders of their fields. It explores the connections of Randomness to other areas of scientific knowledge, especially its fruitful relationship to Computability and Complexity Theory, and also to areas such as Probability, Statistics, Information Theory, Biology, Physics, Quantum Mechanics, Learning Theory and Artificial Intelligence. The contributors cover these topics without neglecting important philosophical dimensions, sometimes going beyond the purely technical to formulate age old questions relating to matters such as determinism and free will.The scope of Randomness Through Computation is novel. Each contributor shares their personal views and anecdotes on the various reasons and motivations which led them to the study of Randomness. Using a question and answer format, they share their visions from their several distinctive vantage points.
Randomness as Circuit Complexity (and the Connection to Pseudorandomness) (E Allender); Randomness Everywhere: My Path to Algorithmic Information Theory (C S Calude); Metaphysics, Metamathematics and Metabiology (G Chaitin); Computability, Algorithmic Randomness and Complexity (R G Downey); Universal Structures Out of Randomness (P Gacs); Is Randomness Necessary? (R Graham); Algorithmic Randomness as Foundation of Inductive Reasoning and Artificial Intelligence (M Hutter); Randomness: A Tool for Constructing and Analyzing Computer Programs (A Kucera); Connecting Randomness to Computation (M Li); Some Bridging Results and Challenges in Classical, Quantum and Computational Randomness (G Longo et al.); Randomness, Computability and Information (J S Miller); Studying Randomness Through Computation (A Nies); Statistical Testing of Randomness: New and Old Procedures (A L Rukhin); Randomness, Occam's Razor, AI, Creativity and Digital Physics (J Schmidhuber); Algorithmic Probability - Its Discovery - Its Properties and Application to Strong AI (R J Solomonoff); From Error-correcting Codes to Algorithmic Information Theory (L Staiger); Uncertainty in Physics and Computation (M A Stay); Indeterminism and Randomness Through Physics (K Svozil); Probability is a Lot of Logic at Once: If You Don't Know Which to Pick, Get'em All (T Toffoli); Randomness in Algorithms (O Watanabe); The Road to Intrinsic Randomness (S Wolfram).