Approximations of Algorithmic and Structural Complexity Validate Cognitive-behavioural Experimental Results

We apply methods for estimating the algorithmic complexity of sequences to behavioural sequences of three landmark studies of animal behavior each of increasing sophistication, including foraging communication by ants, flight patterns of fruit flies, and tactical deception and competition strategies in rodents. In each case, we demonstrate that approximations of Logical Depth and Kolmogorv-Chaitin complexity capture and validate previously reported results, in contrast to other measures such as Shannon Entropy, compression or ad hoc. Our method is practically useful when dealing with short sequences, such as those often encountered in cognitive-behavioural research. Our analysis supports and reveals non-random behavior (LD and K complexity) in flies even in the absence of external stimuli, and confirms the "stochastic" behaviour of transgenic rats when faced that they cannot defeat by counter prediction. The method constitutes a formal approach for testing hypotheses about the mechanisms underlying animal behaviour.Comment: 28 pages, 7 figures and 2 table

Application of Kolmogorov complexity and universal codes to identity testing and nonparametric testing of serial independence for time series

We show that Kolmogorov complexity and such its estimators as universal codes (or data compression methods) can be applied for hypotheses testing in a framework of classical mathematical statistics. The methods for identity testing and nonparametric testing of serial independence for time series are suggested.Comment: submitte

On the Algorithmic Nature of the World

We propose a test based on the theory of algorithmic complexity and an experimental evaluation of Levin's universal distribution to identify evidence in support of or in contravention of the claim that the world is algorithmic in nature. To this end we have undertaken a statistical comparison of the frequency distributions of data from physical sources on the one hand--repositories of information such as images, data stored in a hard drive, computer programs and DNA sequences--and the frequency distributions generated by purely algorithmic means on the other--by running abstract computing devices such as Turing machines, cellular automata and Post Tag systems. Statistical correlations were found and their significance measured.Comment: Book chapter in Gordana Dodig-Crnkovic and Mark Burgin (eds.) Information and Computation by World Scientific, 2010. (http://www.idt.mdh.se/ECAP-2005/INFOCOMPBOOK/). Paper website: http://www.mathrix.org/experimentalAIT

Algorithmic Complexity for Short Binary Strings Applied to Psychology: A Primer

Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them focuses on one feature of randomness, leading authors to have to use multiple measures. Here we describe and advocate for the use of the accepted universal measure for randomness based on algorithmic complexity, by means of a novel previously presented technique using the the definition of algorithmic probability. A re-analysis of the classical Radio Zenith data in the light of the proposed measure and methodology is provided as a study case of an application.Comment: To appear in Behavior Research Method