Kolmogorov Complexity and Algorithmic Randomness
نویسنده
چکیده
This paper aims to provide a minimal introduction to algorithmic randomness. In particular, we cover the equivalent 1-randomness and MartinLöf randomness. After a brief review of relevant concepts in computability, we develop the basic theory of Kolmogorov complexity, including the KC theorem and more general notion of information content measures. We then build two natural definitions of randomness for infinite strings (or reals) and, using the preceding results, prove their equivalence. Finally, we cover an interesting consequence of this equivalence, namely, that almost all reals are 1-random.
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