Abstract
The question how and why mathematical probability theory can be applied to the “real world” has been debated for centuries. We try to survey the role of algorithmic information theory (Kolmogorov complexity) in this debate.
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References
Bienvenu, L., Shen, A.: Algorithmic information theory and martingales, preprint, arXiv:0906.2614
Borel, E.: Le hazard, Alcan, Paris (1914), Russian translation: Gosizdat, Moscow – Petrograd (1923)
Borel, E.: Probabilité et certitude, Presse Univ. de France, Paris (1950), English translation: Probability and certainty, Walker publishers (1963), Russian translation: Fizmatgiz, Moscow (1961)
Goldreich, O.: Foundations of Cryptography. Basic Tools, vol. 1. Cambridge University Press, Cambridge (2007)
Polya, G.: Mathematics and Plausible Reasoning, vol. 1,2. Princeton University Press, Princeton (1990) (reprint)
Renyi, A.: Letters on probability. Wayne State University Press (1972)
Uspensky, V., Semenov, A., Shen, A.: Can an individual sequence of zeros and ones be random? Russian Mathematical Surveys 45(1), 121–189 (1990)
Shen, A.: On the logical basis of application of probability theory. In: Proc. Workshop on semiotic aspects of the formalization of intellectual activity, Telavi (Georgia, then USSR), VINITI, Moscow, pp. 144–146 (1983)
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Shen, A. (2009). Algorithmic Information Theory and Foundations of Probability. In: Bournez, O., Potapov, I. (eds) Reachability Problems. RP 2009. Lecture Notes in Computer Science, vol 5797. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04420-5_4
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DOI: https://doi.org/10.1007/978-3-642-04420-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04419-9
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