The Limits of Decidable States on Open-Ended Evolution and Emergence

Hernández-Orozco, Santiago; Hernández-Quiroz, Francisco; Zenil, Héctor

doi:10.7551/978-0-262-33936-0-ch039

Cited by 4 publications

(3 citation statements)

References 31 publications

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“…• Coding Theorem Method (CTM) as an estimator of algorithmic randomness by way of algorithmic probability via the algorithmic Coding theorem (see Supplementary Material) relating causal content and classical probability (38,39). • Logical Depth (LD) as a BDM-based (see below) estimation of logical depth (30), a measure of sophistication that assigns both algorithmically simple and algorithmically random sequences shallow depth, and everything else higher complexity, believed to be related to biological evolution (31,32).…”

Section: • Lossless Compression (Compress)mentioning

confidence: 99%

Training-free measures based on algorithmic probability identify high nucleosome occupancy in DNA sequences

Zenil

Mináry

2019

Nucleic Acids Research

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We introduce and study a set of training-free methods of an information-theoretic and algorithmic complexity nature that we apply to DNA sequences to identify their potential to identify nucleosomal binding sites. We test the measures on well-studied genomic sequences of different sizes drawn from different sources. The measures reveal the known in vivo versus in vitro predictive discrepancies and uncover their potential to pinpoint high and low nucleosome occupancy. We explore different possible signals within and beyond the nucleosome length and find that the complexity indices are informative of nucleosome occupancy. We found that, while it is clear that the gold standard Kaplan model is driven by GC content (by design) and by k-mer training; for high occupancy, entropy and complexity-based scores are also informative and can complement the Kaplan model.

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Section: • Lossless Compression (Compress)mentioning

confidence: 99%

Training-free measures based on algorithmic probability identify high nucleosome occupancy in DNA sequences

Zenil

Mináry

2019

Nucleic Acids Research

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“…In a previous result [11], we have shown that Chaitin's model exhibits open-ended evolution (OEE [12]) according to a formal definition of OEE as defined in [11] in accordance to the general intuition about OEE, and that no decidable system with computable dynamics can achieve OEE under such computational definition. Here we will introduce a system that, by following the Universal Distribution, optimally approaches OEE.…”

Section: Chaitin's Evolutionary Modelmentioning

confidence: 71%

Algorithmically probable mutations reproduce aspects of evolution, such as convergence rate, genetic memory and modularity

2018

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Natural selection explains how life has evolved over millions of years from more primitive forms. The speed at which this happens, however, has sometimes defied formal explanations when based on random (uniformly distributed) mutations. Here, we investigate the application of a simplicity bias based on a natural but algorithmic distribution of mutations (no recombination) in various examples, particularly binary matrices, in order to compare evolutionary convergence rates. Results both on synthetic and on small biological examples indicate an accelerated rate when mutations are not statistically uniform but algorithmically uniform. We show that algorithmic distributions can evolve modularity and genetic memory by preservation of structures when they first occur sometimes leading to an accelerated production of diversity but also to population extinctions, possibly explaining naturally occurring phenomena such as diversity explosions (e.g. the Cambrian) and massive extinctions (e.g. the End Triassic) whose causes are currently a cause for debate. The natural approach introduced here appears to be a better approximation to biological evolution than models based exclusively upon random uniform mutations, and it also approaches a formal version of open-ended evolution based on previous formal results. These results validate some suggestions in the direction that computation may be an equally important driver of evolution. We also show that inducing the method on problems of optimization, such as genetic algorithms, has the potential to accelerate convergence of artificial evolutionary algorithms.

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“…This way, submachines will only be those machines for which there is another non-reducibly "bigger" machine that can decide, at least, what is the output of the former and whether there is an output at all. In particular, this condition proved to be necessary in order to build theoretical models for an open-ended 2 [18] evolution of programs in which the very environment, or "Nature", can be simulated in a computer [1]. Note that every machine that falls under this definition always defines an equivalent total Turing machine (with a signed output corresponding to the case where the submachine does not halt); and every total Turing machine falls under this definition.…”

Section: Turing Submachinesmentioning

confidence: 99%

Relativizing an incompressible number and an incompressible function through subrecursive extensions of Turing machines

Abrahão

2016

Preprint

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We show in this article that uncomputability is also a relative property of subrecursive classes built on a recursive relative incompressible function, which acts as a higher-order "yardstick" of irreducible information for the respective subrecursive class. We define the concept of a Turing submachine, and a recursive relative version for the Busy Beaver function and for the halting probability (or Chaitin's constant) Ω; respectively the Busy Beaver Plus (BBP) function and a time-bounded halting probability. Therefore, we prove that the computable BBP function defined on any Turing submachine is neither computable nor compressible by any program running on this submachine. In addition, we build a Turing submachine that can use lower approximations to its own time-bounded halting probability to calculate the values of its Busy Beaver Plus function, in the "same" manner that universal Turing machines use approximations to Ω to calculate Busy Beaver values. Thus, the algorithmic information carried by the BBP function is relatively incompressible (and uncomputable) at the same time that it still is occasionally reached by submachines. We point that this phenomenon enriches the research on the relativization and simulation of uncomputability and irreducible information.

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The Limits of Decidable States on Open-Ended Evolution and Emergence

Cited by 4 publications

References 31 publications

Training-free measures based on algorithmic probability identify high nucleosome occupancy in DNA sequences

Training-free measures based on algorithmic probability identify high nucleosome occupancy in DNA sequences

Algorithmically probable mutations reproduce aspects of evolution, such as convergence rate, genetic memory and modularity

Relativizing an incompressible number and an incompressible function through subrecursive extensions of Turing machines

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