Hector Zenil
University of Oxford
Network
Latest external collaboration on country level. Dive into details by clicking on the dots.
Publication
Featured researches published by Hector Zenil.
PeerJ | 2015
Hector Zenil; Fernando Soler-Toscano; Jean-Paul Delahaye; Nicolas Gauvrit
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating n-dimensional complexity by using an n-dimensional deterministic Turing machine. The technique is interesting because it provides a natural algorithmic process for symmetry breaking generating complex n-dimensional structures from perfectly symmetric and fully deterministic computational rules producing a distribution of patterns as described by algorithmic probability. Algorithmic probability also elegantly connects the frequency of occurrence of a pattern with its algorithmic complexity, hence eff ectively providing estimations to the complexity of the generated patterns. Experiments to validate estimations of algorithmic complexity based on these concepts are presented, showing that the measure is stable in the face of some changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms when both methods overlap in their range of applicability. We then use the output frequency of the set of 2-dimensional Turing machines to classify the algorithmic complexity of the space-time evolutions of Elementary Cellular Automata.
PLOS Computational Biology | 2017
Nicolas Gauvrit; Hector Zenil; Fernando Soler-Toscano; Jean-Paul Delahaye; Peter Brugger
Random Item Generation tasks (RIG) are commonly used to assess high cognitive abilities such as inhibition or sustained attention. They also draw upon our approximate sense of complexity. A detrimental effect of aging on pseudo-random productions has been demonstrated for some tasks, but little is as yet known about the developmental curve of cognitive complexity over the lifespan. We investigate the complexity trajectory across the lifespan of human responses to five common RIG tasks, using a large sample (n = 3429). Our main finding is that the developmental curve of the estimated algorithmic complexity of responses is similar to what may be expected of a measure of higher cognitive abilities, with a performance peak around 25 and a decline starting around 60, suggesting that RIG tasks yield good estimates of such cognitive abilities. Our study illustrates that very short strings of, i.e., 10 items, are sufficient to have their complexity reliably estimated and to allow the documentation of an age-dependent decline in the approximate sense of complexity.
International Journal of Parallel, Emergent and Distributed Systems | 2018
Hector Zenil; Liliana Badillo; Santiago Hernández-Orozco; Francisco Hernández-Quiroz
ABSTRACT Previously referred to as ‘miraculous’ in the scientific literature because of its powerful properties and its wide application as optimal solution to the problem of induction/inference, (approximations to) Algorithmic Probability (AP) and the associated Universal Distribution are (or should be) of the greatest importance in science. Here we investigate the emergence, the rates of emergence and convergence, and the Coding-theorem like behaviour of AP in Turing-subuniversal models of computation. We investigate empirical distributions of computing models in the Chomsky hierarchy. We introduce measures of algorithmic probability and algorithmic complexity based upon resource-bounded computation, in contrast to previously thoroughly investigated distributions produced from the output distribution of Turing machines. This approach allows for numerical approximations to algorithmic (Kolmogorov-Chaitin) complexity-based estimations at each of the levels of a computational hierarchy. We demonstrate that all these estimations are correlated in rank and that they converge both in rank and values as a function of computational power, despite fundamental differences between computational models. In the context of natural processes that operate below the Turing universal level because of finite resources and physical degradation, the investigation of natural biases stemming from algorithmic rules may shed light on the distribution of outcomes. We show that up to 60% of the simplicity/complexity bias in distributions produced even by the weakest of the computational models can be accounted for by Algorithmic Probability in its approximation to the Universal Distribution.
arXiv: Computational Engineering, Finance, and Science | 2017
Hector Zenil
This is a review of aspects of the theory of algorithmic information that may contribute to a framework for formulating questions related to complex, highly unpredictable systems. We start by contrasting Shannon entropy and Kolmogorov-Chaitin complexity, which epitomize correlation and causation respectively, and then surveying classical results from algorithmic complexity and algorithmic probability, highlighting their deep connection to the study of automata frequency distributions. We end by showing that though long-range algorithmic prediction models for economic and biological systems may require infinite computation, locally approximated short-range estimations are possible, thereby demonstrating how small data can deliver important insights into important features of complex “Big Data”.
Complexity | 2017
Fernando Soler-Toscano; Hector Zenil
We study formal properties of a Levin-inspired measure
Royal Society Open Science | 2018
Santiago Hernández-Orozco; Narsis A. Kiani; Hector Zenil
m
arXiv: Computational Complexity | 2017
Hector Zenil; Jürgen Riedel
calculated from the output distribution of small Turing machines. We introduce and justify finite approximations
Entropy | 2018
Hector Zenil; Narsis A. Kiani; Jesper Tegnér
m_k
Entropy | 2018
Hector Zenil; Narsis A. Kiani; Jesper Tegnér
that have already been used in applications as an alternative to lossless compression algorithms for approximating algorithmic (Kolmogorov-Chaitin) complexity. We provide proofs of the relevant properties of both
conference on computability in europe | 2017
Alberto Hernández-Espinosa; Francisco Hernández-Quiroz; Hector Zenil
m