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Classification of Discrete Dynamical Systems Based on Transients

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Barbora Hudcová, Tomáš Mikolov

Artificial Intelligence · Submitted 3 Aug 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We were able to identify a critical region of behavior that corresponds to a phase transition from ordered behavior to chaos across various classes of dynamical systems.

how it is stated · asserted 1.00 read the record →

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arXiv ID2108.01573 (version 1)
Pith IDILXG3G6H, Pith's permanent record of this paper and its review
CitationBarbora Hudcov\'a, Tom\'a\v{s} Mikolov. "Classification of Discrete Dynamical Systems Based on Transients." arXiv:2108.01573 (2021). https://pith.science/paper/ILXG3G6H
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,190 input tokens.

What the abstract itself states, as probabilities: claims first 0.21 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.42 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical systems. The method is based on classifying the asymptotic behavior of the average computation time in a given system before entering a loop. We were able to identify a critical region of behavior that corresponds to a phase transition from ordered behavior to chaos across various classes of dynamical systems. To show that our approach can be applied to many different computational systems, we demonstrate the results of classifying cellular automata, Turing machines, and random Boolean networks. Further, we use this method to classify 2D cellular automata to automatically find those with interesting, complex dynamics. We believe that our work can be used to design systems in which complex structures emerge. Also, it can be used to compare various versions of existing attempts to model open-ended evolution (Ray (1991), Ofria et al. (2004), Channon (2006)).

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. background 0.99 0.05 0.03 asserted 0.97
s1 We present a novel classification method applicable to any class of deterministic discrete space and time dynamical systems. contribution 0.98 0.89 0.10 asserted 1.00
s2 The method is based on classifying the asymptotic behavior of the average computation time in a given system before entering a loop. method 0.99 0.53 0.08 asserted 1.00
s3 We were able to identify a critical region of behavior that corresponds to a phase transition from ordered behavior to chaos across various classes of dynamical systems. result 0.99 0.96 0.60 asserted 1.00
s4 To show that our approach can be applied to many different computational systems, we demonstrate the results of classifying cellular automata, Turing machines, and random Boolean networks. contribution 0.66 0.95 0.07 asserted 1.00
s5 Further, we use this method to classify 2D cellular automata to automatically find those with interesting, complex dynamics. contribution 0.87 0.95 0.11 asserted 1.00
s6 We believe that our work can be used to design systems in which complex structures emerge. interpretation 0.54 0.10 0.26 hedged possibility 0.81
s7 Also, it can be used to compare various versions of existing attempts to model open-ended evolution (Ray (1991), Ofria et al. (2004), Channon (2006)). future work 0.64 0.54 0.06 hedged possibility 0.72

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
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  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical systems. The method is based on classifying the asymptotic behavior of the average computation time in a given system before entering a loop. We were able to identify a critical region of behavior that corresponds to a phase transition from ordered behavior to chaos across various classes of dynamical systems. To show that our approach can be applied to many different computational systems, we demonstrate the results of classifying cellular automata, Turing machines, and random Boolean networks. Further, we use this method to classify 2D cellular automata to automatically find those with interesting, complex dynamics. We believe that our work can be used to design systems in which complex structures emerge. Also, it can be used to compare various versions of existing attempts to model open-ended evolution (Ray (1991), Ofria et al. (2004), Channon (2006)).

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