Abstract
The notion of Kolmogorov algorithmic complexity of sequences of symbols is used to define pseudo-random sequences of stochastically independent and identically distributed samples from a finite set and pseudo-Markov chains with a finite set of states. Sufficient conditions are introduced and discussed, under which the ideas used in these two special cases can be generalized to obtain an appropriate complexity-based definition of pseudo-random sequences with a more complicated stochastical structure.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Davis M. (1958): Computability and Unsolvability. McGraw-Hill Book Comp., New York.
Fine T. L. (1973): Theories of Probability - an Examination of Foundations. Academic Press, New York - London.
Kolmogorov A. N. (1965): Three Approaches to the Quantitative Definition of Information. Problemy peredači informacii vol. 1, no. 1, pp. 4–7.
Kramosil I. (1983): Monte-Carlo Methods from the Point of View of Algorithmic Complexity. In: Trans, of the 9-th Prague Conference on Information Theory,…, 1982. Academia, Prague, pp. 39–51.
Kramosil I. (1984) Recursive Classification of Pseudo-Random Sequences. Kybernetika, vol. 20 - supplement, pp. 1–34.
Kramosil I. (1985) Pseudo-markovské posloupnosti (Pseudo-Markov Sequences - in Czech). Res. Rep. no. 1328, Inst. of Inf. Theory and Automation.
Kramosil I. (1986a): Independent and Identically Distributed Pseudo-Random Samples. To appear in Kybernetika (Prague).
Kramosil I. (1986b): On Some Types of Pseudo-Random Sequences. To appear in MFCS 86 Proceedings.
Kramosil I., Šindelář J. (1984): Infinite Pseudo-Random Sequences of High Algorithmic Complexity. Kybernetika, vol. 20, no. 6, pp. 429–437.
Martin-Löf P. (1966): The Definition of Random Sequences. Information and Control, vol. 9, no. 3, pp. 602–619.
von Mises R. (1919): Grundlangen der Wahrscheinlichkeitsrechnung. Math.Zeitschrift vol. 5, pp. 52–99.
Rogers H. (1967): Theory of Recursive Functions and Effective Computability. McGraw-Hill Book Comp., New York.
Schnorr C.-P. (1971): Zufälligskeit und Wahrscheinlichkeit. Lect. Notes in Math. 218, Springer-Verlag, Berlin- -Heidelberg-New York.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Academia, Publishing House of the Czechoslovak Academy of Sciences, Prague
About this chapter
Cite this chapter
Kramosil, I. (1988). Algorithmic Complexity and Pseudo-Random Sequences. In: Višek, J.Á. (eds) Transactions of the Tenth Prague Conference. Czechoslovak Academy of Sciences, vol 10A-B. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3859-5_5
Download citation
DOI: https://doi.org/10.1007/978-94-009-3859-5_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8216-7
Online ISBN: 978-94-009-3859-5
eBook Packages: Springer Book Archive