Abstract
In this chapter, we present a ”non-classical” definition of randomness that is of a quite different nature from the other criteria in the previous chapters. Namely, loosely speaking, a bitstring can be called ”random”, if the shortest program (in the sense of a Turing machine) for describing the string is the string itself. The length of this shortest program can be viewed as some sort of ”algorithmic complexity” measure, which itself is of rather theoretical value, but one can show that it is indeed in ”most” cases closely related to the linear complexity. So somewhat surprisingly, for ”most” cases (in a measure-theoretic sense to be specified), the linear complexity seems to be a ”universal” randomness criterion! (However, this definition does not apply to individual sequences!)
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Neuenschwander, D. (2004). 11 *Algorithmic Complexity. In: Probabilistic and Statistical Methods in Cryptology. Lecture Notes in Computer Science, vol 3028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25942-8_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-25942-8_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22001-5
Online ISBN: 978-3-540-25942-8
eBook Packages: Springer Book Archive