edited by Hector Zenil (Wolfram Research Inc., USA)

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.

• Stochastic Randomness and Probabilistic Deliberations:
  • Is Randomness Necessary? (R Graham)
  • Probability is a Lot of Logic at Once: If You Don't Know Which One to Pick, Get'em All (T Toffoli)
  • Statistical Testing of Randomness: New and Old Procedures (A L Rukhin)
  • Scatter and Regularity Imply Benford's Law… and More (N Gauvrit & J-P Delahaye)
• Randomness and computation in connection to the Physical world:
  • Some Bridging Results and Challenges in Classical, Quantum and Computational Randomness (G Longo et al.)
  • Metaphysics, Metamathematics and Metabiology (G Chaitin)
  • Uncertainty in Physics and Computation (M A Stay)
  • Indeterminism and Randomness Through Physics (K Svozil)
  • The Martin-Löf-Chaitin Thesis: The Identification by Recursion Theory of the Mathematical Notion of Random Sequence (J-P Delahaye)
  • The Road to Intrinsic Randomness (S Wolfram)
• Algorithmic Inference and Artificial Intelligence:
  • Algorithmic Probability — Its Discovery — Its Properties and Application to Strong AI (R J Solomonoff)
  • Algorithmic Randomness as Foundation of Inductive Reasoning and Artificial Intelligence (M Hutter)
  • Randomness, Occam's Razor, AI, Creativity and Digital Physics (J Schmidhuber)
  • Randomness Everywhere: My Path to Algorithmic Information Theory (C S Calude)
  • The Impact of Algorithmic Information Theory on Our Current Views on Complexity, Randomness, Information and Prediction (P Gács)
  • Randomness, Computability and Information (J S Miller)
  • Studying Randomness Through Computation (A Nies)
  • Computability, Algorithmic Randomness and Complexity (R G Downey)
  • Is Randomness Native to Computer Science? Ten Years After (M Ferbus-Zanda & S Grigorieff)
• Computational Complexity, Randomized Algorithms and Applications:
  • Randomness as Circuit Complexity (and the Connection to Pseudorandomness) (E Allender)
  • Randomness: A Tool for Constructing and Analyzing Computer Programs (A Kučera)
  • Connecting Randomness to Computation (M Li)
  • From Error-correcting Codes to Algorithmic Information Theory (L Staiger)
  • Randomness in Algorithms (O Watanabe)
  • Is the Universe Random? (C S Calude et al.)
  • What is Computation? (How) Does Nature Compute? (C S Calude et al.)