scholarly journals Algorithmic probability

Scholarpedia ◽  
2007 ◽  
Vol 2 (8) ◽  
pp. 2572 ◽  
Author(s):  
Marcus Hutter ◽  
Shane Legg ◽  
Paul Vitanyi
Keyword(s):  
Algorithmic Probability

scholarly journals Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 534 ◽  
Author(s):  
Hector Zenil ◽  
Narsis Kiani ◽  
Jesper Tegnér
Keyword(s):  
Algorithmic Complexity ◽  
Information Theoretic ◽  
Algorithmic Probability ◽  
Graphs And Networks ◽  
Algorithmic Information ◽  
Statistical Regularities ◽  
Review Study ◽  
Causal Nature ◽  
Definition Of

We introduce a definition of algorithmic symmetry in the context of geometric and spatial complexity able to capture mathematical aspects of different objects using as a case study polyominoes and polyhedral graphs. We review, study and apply a method for approximating the algorithmic complexity (also known as Kolmogorov–Chaitin complexity) of graphs and networks based on the concept of Algorithmic Probability (AP). AP is a concept (and method) capable of recursively enumerate all properties of computable (causal) nature beyond statistical regularities. We explore the connections of algorithmic complexity—both theoretical and numerical—with geometric properties mainly symmetry and topology from an (algorithmic) information-theoretic perspective. We show that approximations to algorithmic complexity by lossless compression and an Algorithmic Probability-based method can characterize spatial, geometric, symmetric and topological properties of mathematical objects and graphs.

Algorithmic Probability: A Collection of Problems.

1996 ◽  
Vol 91 (434) ◽  
pp. 915
Author(s):  
Paul Embrechts ◽  
Marcel F. Neuts
Keyword(s):  
Algorithmic Probability
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