scholarly journals Computational universality of fungal sandpile automata

2020 ◽  
Vol 384 (22) ◽  
pp. 126541
Author(s):  
Eric Goles ◽  
Michail-Antisthenis Tsompanas ◽  
Andrew Adamatzky ◽  
Martin Tegelaar ◽  
Han A.B. Wosten ◽  
...  
Keyword(s):  
Computational Universality

Phase Transition in Elementary Cellular Automata with Memory

2014 ◽  
Vol 24 (09) ◽  
pp. 1450116 ◽  
Author(s):  
Shigeru Ninagawa ◽  
Andrew Adamatzky ◽  
Ramón Alonso-Sanz
Keyword(s):  
Cellular Automata ◽  
State Transition ◽  
Time Interval ◽  
Complex Behavior ◽  
Weighted Function ◽  
Transition Functions ◽  
Elementary Cellular Automata ◽  
Computational Universality ◽  
With Memory ◽  
Time Automaton

We study elementary cellular automata with memory. The memory is a weighted function averaged over cell states in a time interval, with a varying factor which determines how strongly a cell's previous states contribute to the cell's present state. We classify selected cell-state transition functions based on Lempel–Ziv compressibility of space-time automaton configurations generated by these functions and the spectral analysis of their transitory behavior. We focus on rules 18, 22, and 54 because they exhibit the most intriguing behavior, including computational universality. We show that a complex behavior is observed near the nonmonotonous transition to null behavior (rules 18 and 54) or during the monotonic transition from chaotic to periodic behavior (rule 22).

Cognitive architectures need compliancy, not universality

2003 ◽  
Vol 26 (5) ◽  
pp. 628-628
Author(s):  
Richard M. Young
Keyword(s):  
Cognitive Architectures ◽  
Computational Universality

The criterion of computational universality for an architecture should be replaced by the notion of compliancy, where a model built within an architecture is compliant to the extent that the model allows the architecture to determine the processing. The test should be that the architecture does easily – that is, enables a compliant model to do – what people do easily.

scholarly journals Computational Power of Asynchronously Tuned Automata Enhancing the Unfolded Edge of Chaos

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1376
Author(s):  
Yukio-Pegio Gunji ◽  
Daisuke Uragami
Keyword(s):  
Phase Transition ◽  
Cellular Automata ◽  
Dissipative Structure ◽  
Quantitative Measure ◽  
Computational Power ◽  
Critical Property ◽  
Edge Of Chaos ◽  
Computational Universality ◽  
Asynchronous Updating ◽  
The Relationship

Asynchronously tuned elementary cellular automata (AT-ECA) are described with respect to the relationship between active and passive updating, and that spells out the relationship between synchronous and asynchronous updating. Mutual tuning between synchronous and asynchronous updating can be interpreted as the model for dissipative structure, and that can reveal the critical property in the phase transition from order to chaos. Since asynchronous tuning easily makes behavior at the edge of chaos, the property of AT-ECA is called the unfolded edge of chaos. The computational power of AT-ECA is evaluated by the quantitative measure of computational universality and efficiency. It shows that the computational efficiency of AT-ECA is much higher than that of synchronous ECA and asynchronous ECA.

scholarly journals Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 228 ◽  
Author(s):  
Austin K. Daniel ◽  
Rafael N. Alexander ◽  
Akimasa Miyake
Keyword(s):  
Cellular Automata ◽  
Error Correction ◽  
Quantum Computation ◽  
Cluster State ◽  
Quantum Cellular Automata ◽  
Fine Grained ◽  
Computational Capability ◽  
Lattice Geometry ◽  
Computational Universality ◽  
Symmetry Protected

What kinds of symmetry-protected topologically ordered (SPTO) ground states can be used for universal measurement-based quantum computation in a similar fashion to the 2D cluster state? 2D SPTO states are classified not only by global on-site symmetries but also by subsystem symmetries, which are fine-grained symmetries dependent on the lattice geometry. Recently, all states within so-called SPTO cluster phases on the square and hexagonal lattices have been shown to be universal, based on the presence of subsystem symmetries and associated structures of quantum cellular automata. Motivated by this observation, we analyze the computational capability of SPTO cluster phases on all vertex-translative 2D Archimedean lattices. There are four subsystem symmetries here called ribbon, cone, fractal, and 1-form symmetries, and the former three are fundamentally in one-to-one correspondence with three classes of Clifford quantum cellular automata. We conclude that nine out of the eleven Archimedean lattices support universal cluster phases protected by one of the former three symmetries, while the remaining lattices possess 1-form symmetries and have a different capability related to error correction.

scholarly journals Parallel Multiset Rewriting Systems with Distorted Rules

Processes ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 347
Author(s):  
Cristina Sburlan ◽  
Dragoş-Florin Sburlan
Keyword(s):  
A Priori ◽  
Rewriting Systems ◽  
Computational Universality ◽  
Level 1 ◽  
Robust Systems ◽  
Rewriting Rules

Most of the parallel rewriting systems which model (or which are inspired by) natural/artificial phenomena consider fixed, a priori defined sets of string/multiset rewriting rules whose definitions do not change during the computation. Here we modify this paradigm by defining level-t distorted rules—rules for which during their applications one does not know the exact multiplicities of at most t∈N species of objects in their output (although one knows that such objects will appear at least once in the output upon the execution of this type of rules). Subsequently, we define parallel multiset rewriting systems with t-distorted computations and we study their computational capabilities when level-1 distorted catalytic promoted rules are used. We construct robust systems able to cope with the level-1 distortions and prove the computational universality of the model.

scholarly journals Life Worth Mentioning: Complexity in Life-Like Cellular Automata

2021 ◽  
Vol 27 (2) ◽  
pp. 105-112
Author(s):  
Eric Peña ◽  
Hiroki Sayama
Keyword(s):  
Cellular Automata ◽  
Quantitative Comparison ◽  
High Density ◽  
Optimal Complexity ◽  
Complex Dynamic ◽  
Game Of Life ◽  
Basic Ingredient ◽  
Computational Universality ◽  
Global Patterns ◽  
Dynamic Patterns

Abstract Cellular automata (CA) have been lauded for their ability to generate complex global patterns from simple local rules. The late English mathematician, John Horton Conway, developed his illustrious Game of Life (Life) CA in 1970, which has since remained one of the most quintessential CA constructions—capable of producing a myriad of complex dynamic patterns and computational universality. Life and several other Life-like rules have been classified in the same group of aesthetically and dynamically interesting CA rules characterized by their complex behaviors. However, a rigorous quantitative comparison among similarly classified Life-like rules has not yet been fully established. Here we show that Life is capable of maintaining as much complexity as similar rules while remaining the most parsimonious. In other words, Life contains a consistent amount of complexity throughout its evolution, with the least number of rule conditions compared to other Life-like rules. We also found that the complexity of higher density Life-like rules, which themselves contain the Life rule as a subset, form a distinct concave density-complexity relationship whereby an optimal complexity candidate is proposed. Our results also support the notion that Life functions as the basic ingredient for cultivating the balance between structure and randomness to maintain complexity in 2D CA for low- and high-density regimes, especially over many iterations. This work highlights the genius of John Horton Conway and serves as a testament to his timeless marvel, which is referred to simply as: Life.

Sign in / Sign up

Export Citation Format

Share Document