A review of methods for estimating algorithmic complexity: options, challenges, and new directions

H Zenil - Entropy, 2020 - mdpi.com
Some established and also novel techniques in the field of applications of algorithmic
(Kolmogorov) complexity currently co-exist for the first time and are here reviewed, ranging …

Calculating Kolmogorov complexity from the output frequency distributions of small Turing machines

F Soler-Toscano, H Zenil, JP Delahaye, N Gauvrit - PloS one, 2014 - journals.plos.org
Drawing on various notions from theoretical computer science, we present a novel
numerical approach, motivated by the notion of algorithmic probability, to the problem of …

A decomposition method for global evaluation of Shannon entropy and local estimations of algorithmic complexity

H Zenil, S Hernández-Orozco, NA Kiani… - Entropy, 2018 - mdpi.com
We investigate the properties of a Block Decomposition Method (BDM), which extends the
power of a Coding Theorem Method (CTM) that approximates local estimations of …

Numerical evaluation of algorithmic complexity for short strings: A glance into the innermost structure of randomness

JP Delahaye, H Zenil - Applied Mathematics and Computation, 2012 - Elsevier
We describe an alternative method (to compression) that combines several theoretical and
experimental results to numerically approximate the algorithmic Kolmogorov–Chaitin …

Compression-based investigation of the dynamical properties of cellular automata and other systems

H Zenil - arXiv preprint arXiv:0910.4042, 2009 - arxiv.org
A method for studying the qualitative dynamical properties of abstract computing machines
based on the approximation of their program-size complexity using a general lossless …

East-West paths to unconventional computing

A Adamatzky, S Akl, M Burgin, CS Calude… - Progress in biophysics …, 2017 - Elsevier
Unconventional computing is about breaking boundaries in thinking, acting and computing.
Typical topics of this non-typical field include, but are not limited to physics of computation …

An algorithmic information calculus for causal discovery and reprogramming systems

H Zenil, NA Kiani, F Marabita, Y Deng, S Elias… - Iscience, 2019 - cell.com
We introduce and develop a method that demonstrates that the algorithmic information
content of a system can be used as a steering handle in the dynamical phase space, thus …

Two-dimensional Kolmogorov complexity and an empirical validation of the Coding theorem method by compressibility

H Zenil, F Soler-Toscano, JP Delahaye… - PeerJ Computer …, 2015 - peerj.com
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 …

Algorithmic thermodynamics

J Baez, M Stay - Mathematical Structures in Computer Science, 2012 - cambridge.org
Algorithmic entropy can be viewed as a special case of the entropy studied in statistical
mechanics. This viewpoint allows us to apply many techniques developed for use in …

Estimating algorithmic information using quantum computing for genomics applications

A Sarkar, Z Al-Ars, K Bertels - Applied Sciences, 2021 - mdpi.com
Inferring algorithmic structure in data is essential for discovering causal generative models.
In this research, we present a quantum computing framework using the circuit model, for …