Algorithmic Information Theory

Classical information theory is concerned with Random Process es, but it makes little sense to call the end result of a process "random" without the context of what process produced it. For example, the process of flipping a coin produces the outcomes "heads" and "tails", but it is absurd to claim that "heads" is a random side of a coin, or that "heads", "tails" is random outcome for flipping three coins. In contrast, algorithmic information theory uses the existence of Universal Computers to define certain objects as inherently random or nonrandom. In particular, algorithmic information theory gives formal, rigorous definitions of a Random String and a Random Infinite Sequence .

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Kolmogorov Complexity

Algorithmically Random Sequence

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Algorithmic Information Theory