TY - JOUR
UR - https://doi.org/10.7717/peerj-cs.23
DO - 10.7717/peerj-cs.23
TI - Two-dimensional Kolmogorov complexity and an empirical validation of the Coding theorem method by compressibility
AU - Zenil,Hector
AU - Soler-Toscano,Fernando
AU - Delahaye,Jean-Paul
AU - Gauvrit,Nicolas
A2 - Skoglund,Mikael
DA - 2015/09/30
PY - 2015
KW - Algorithmic complexity
KW - Algorithmic probability
KW - Kolmogorovâ€“Chaitin complexity
KW - Algorithmic information theory
KW - Cellular automata
KW - Solomonoffâ€“Levin universal distribution
KW - Information theory
KW - Dimensional complexity
KW - Image complexity
KW - Small Turing machines
AB -
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 effectively 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.
VL - 1
SP - e23
T2 - PeerJ Computer Science
JO - PeerJ Computer Science
J2 - PeerJ Computer Science
SN - 2376-5992
ER -