Computational Hierarchy of Elementary Cellular Automata

@article{Hudcov2021ComputationalHO,
  title={Computational Hierarchy of Elementary Cellular Automata},
  author={Barbora Hudcov{\'a} and Tomas Mikolov},
  journal={ArXiv},
  year={2021},
  volume={abs/2108.00415}
}
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the ability of automata to emulate one another, and we use this notion to define such a set of naturally emerging tasks. We present the results for elementary cellular automata, although the core ideas can be extended to other computational systems. We compute a graph… Expand

Figures and Tables from this paper

References

SHOWING 1-10 OF 32 REFERENCES
Coarse-graining of cellular automata, emergence, and the predictability of complex systems.
TLDR
It is shown that because in practice one only seeks coarse-grained information, complex physical systems can be predictable and even decidable at some level of description, and it is argued that the large-scale dynamics of CA can be very simple, at least when measured by the Kolmogorov complexity of theLarge-scale update rule. Expand
Universality in Elementary Cellular Automata
The purpose of this paper is to prove that one of the simplest one dimensional cellular automata is computationally universal, implying that many questions concerning its behavior, such as whether aExpand
Computation in Cellular Automata: A Selected Review
Cellular automata (CAs) are decentralized spatially extended systems consisting of large numbers of simple identical components with local connectivity. Such systems have the potential to performExpand
Irreducible elementary cellular automata found
TLDR
A novel CG algorithm of substantially lower computational load is presented that can be used both as a valuable tool for theoretical investigations on cellular automata taxonomy and as a useful metaphor of coarse-graining procedures employed to more realistic modeling paradigms such as the particle method. Expand
On the Dynamical Behavior of Chaotic Cellular Automata
TLDR
A new definition of strong topological chaos for discrete time dynamical systems which fulfills the informal intuition of chaotic behavior that everyone has in mind is proposed and it is proved that under this new definition, the bi-infinite shift is no more chaotic. Expand
Inducing an Order on Cellular Automata by a Grouping Operation
TLDR
It is proved that (CA ∗, ⩽) admits a global minimum and that very natural equivalence classes are located at the bottom of (CA⩽), which allows us to conclude that, in a grouping sense, there is no universal CA. Expand
Exact solvability and quasiperiodicity of one-dimensional cellular automata
Cellular automata are a class of mathematical systems characterized by discreteness (in space, time, and state values), determinism, and local interaction. Little is known mathematically aboutExpand
Universality and complexity in cellular automata
TLDR
Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes, and one class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable. Expand
Compression-Based Investigation of the Dynamical Properties of Cellular Automata and Other Systems
  • H. Zenil
  • Computer Science, Mathematics
  • Complex Syst.
  • 2010
TLDR
A conjecture regarding the capability of a system to reach computational universality related to the values of this phase transition coefficient is formulated and these ideas constitute a compression-based framework for investigating the dynamical properties of cellular automata and other systems. Expand
Algebraic properties of cellular automata
Cellular automata are discrete dynamical systems, of simple construction but complex and varied behaviour. Algebraic techniques are used to give an extensive analysis of the global properties of aExpand
...
1
2
3
4
...