Ergodic theorems for individual random sequences
Theoretical Computer Science - Special issue Kolmogorov complexity
Information and Randomness: An Algorithmic Perspective
Information and Randomness: An Algorithmic Perspective
Randomness and determinism in the interplay between the continuum and the discrete†
Mathematical Structures in Computer Science
Computability and information in models of randomness and chaos†
Mathematical Structures in Computer Science
Semiclassical analysis and sensitivity to initial conditions
Information and Computation
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In this text we will discuss different forms of randomness in Natural Sciences and present some recent results relating them. In finite processes, randomness differs in various theoretical context, or, to put it otherwise, there is no unifying notion of finite time randomness. In particular, we will introduce, classical (dynamical), quantum and algorithmic randomness. In physics, differing probabilities, as a measure of randomness, evidentiate the differences between the various notions. Yet, asymptotically , one is universal: Martin-Löf randomness provides a clearly defined and robust notion of randomness for infinite sequences of numbers. And this is based on recursion theory, that is the theory of effective computability. As a recurring issue, the question will be raised of what randomenss means in biology, phylogenesis in particular. Finally, hints will be given towards a thesis, relating finite time randomness and time irreversibility in physical processes.