scholarly journals Stable Multi-Level Monotonic Eroders

2021 ◽  
Author(s):  
Péter Gács ◽  
Ilkka Törmä
Keyword(s):  
Cellular Automata ◽  
Random Noise ◽  
Dimensional Case ◽  
Combinatorial Characterization ◽  
One Dimensional ◽  
Similar Characterization ◽  
Multi Level ◽  
Ordered State

AbstractEroders are monotonic cellular automata with a linearly ordered state set that eventually wipe out any finite island of nonzero states. One-dimensional eroders were studied by Gal’perin in the 1970s, who presented a simple combinatorial characterization of the class. The multi-dimensional case has been studied by Toom and others, but no such characterization has been found. We prove a similar characterization for those one-dimensional monotonic cellular automata that are eroders even in the presence of random noise.

scholarly journals Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant States

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Pabitra Pal Choudhury ◽  
Sudhakar Sahoo ◽  
Mithun Chakraborty
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Boolean Functions ◽  
State Transition ◽  
The State ◽  
Transition Diagram ◽  
One Dimensional ◽  
State Transition Diagram ◽  
Linear Rule

Dynamics of a nonlinear cellular automaton (CA) is, in general asymmetric, irregular, and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable, primarily due to the presence of a matrix handle. In this paper, we present a novel technique of studying the properties of the State Transition Diagram of a nonlinear uniform one-dimensional cellular automaton in terms of its deviation from a suggested linear model. We have considered mainly elementary cellular automata with neighborhood of size three, and, in order to facilitate our analysis, we have classified the Boolean functions of three variables on the basis of number and position(s) of bit mismatch with linear rules. The concept of deviant and nondeviant states is introduced, and hence an algorithm is proposed for deducing the State Transition Diagram of a nonlinear CA rule from that of its nearest linear rule. A parameter called the proportion of deviant states is introduced, and its dependence on the length of the CA is studied for a particular class of nonlinear rules.

Definition and Application of a Five-Parameter Characterization of One-Dimensional Cellular Automata Rule Space

2001 ◽  
Vol 7 (3) ◽  
pp. 277-301 ◽  
Author(s):  
Gina M. B. Oliveira ◽  
Pedro P. B. de Oliveira ◽  
Nizam Omar
Keyword(s):  
Phase Transition ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Dynamic Behavior ◽  
Discrete Dynamical Systems ◽  
Transition Diagram ◽  
One Dimensional ◽  
Rule Space ◽  
Spatially Extended

Cellular automata (CA) are important as prototypical, spatially extended, discrete dynamical systems. Because the problem of forecasting dynamic behavior of CA is undecidable, various parameter-based approximations have been developed to address the problem. Out of the analysis of the most important parameters available to this end we proposed some guidelines that should be followed when defining a parameter of that kind. Based upon the guidelines, new parameters were proposed and a set of five parameters was selected; two of them were drawn from the literature and three are new ones, defined here. This article presents all of them and makes their qualities evident. Then, two results are described, related to the use of the parameter set in the Elementary Rule Space: a phase transition diagram, and some general heuristics for forecasting the dynamics of one-dimensional CA. Finally, as an example of the application of the selected parameters in high cardinality spaces, results are presented from experiments involving the evolution of radius-3 CA in the Density Classification Task, and radius-2 CA in the Synchronization Task.

Complex Order from Disorder and from Simple Order in Coarse-Graining Invariant Orbits of Certain Two-Dimensional Linear Cellular Automata

1997 ◽  
Vol 07 (07) ◽  
pp. 1451-1496 ◽  
Author(s):  
André Barbé
Keyword(s):  
Cellular Automata ◽  
Three Dimensional ◽  
Coarse Graining ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Complex Order ◽  
Simple Order ◽  
Problems And Solutions ◽  
The One

This paper considers three-dimensional coarse-graining invariant orbits for two-dimensional linear cellular automata over a finite field, as a nontrivial extension of the two-dimensional coarse-graining invariant orbits for one-dimensional CA that were studied in an earlier paper. These orbits can be found by solving a particular kind of recursive equations (renormalizing equations with rescaling term). The solution starts from some seed that has to be determined first. In contrast with the one-dimensional case, the seed has infinite support in most cases. The way for solving these equations is discussed by means of some examples. Three categories of problems (and solutions) can be distinguished (as opposed to only one in the one-dimensional case). Finally, the morphology of a few coarse-graining invariant orbits is discussed: Complex order (of quasiperiodic type) seems to emerge from random seeds as well as from seeds of simple order (for example, constant or periodic seeds).

scholarly journals Remarks on the Structure of Clifford Quantum Cellular Automata

2009 ◽  
Vol 16 (02n03) ◽  
pp. 269-279
Author(s):  
Dirk-Michael Schlingemann
Keyword(s):  
Phase Space ◽  
Cellular Automata ◽  
Symplectic Group ◽  
Tensor Products ◽  
Projective Representation ◽  
Dimensional Case ◽  
Additional Restriction ◽  
Quantum Cellular Automata ◽  
One Dimensional ◽  
The One

We report here on the structure of reversible quantum cellular automata with the additional restriction that these are also Clifford operations. This means that tensor products of Weyl operators (projective representation of a finite abelian symplectic group) are mapped to multiples of tensor products of Weyl operators. Therefore Clifford quantum cellular automata are induced by symplectic cellular automata in phase space. We characterize these symplectic cellular automata and find that all possible local rules must be, up to some global shift, reflection-invariant with respect to the origin. In the one-dimensional case we also find that all 1D Clifford quantum cellular automata are generated by a few elementary operations.

GLOBALLY SYNCHRONIZED OSCILLATIONS IN AN ONE-DIMENSIONAL CELLULAR AUTOMATON

2004 ◽  
Vol 15 (03) ◽  
pp. 409-425
Author(s):  
FRANCISCO JIMÉNEZ-MORALES ◽  
MARCO TOMASSINI
Keyword(s):  
Genetic Algorithm ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Random Noise ◽  
Regular Pattern ◽  
Final State ◽  
One Dimensional ◽  
Lattice Size ◽  
Spatial Periodicity ◽  
Temporal Periodicity

Using a genetic algorithm a population of one-dimensional binary cellular automata is evolved to perform a computational task for which the best evolved rules cause the concentration to display a period-three oscillation. One run is studied in which the final state reached by the best evolved rule consists of a regular pattern or domain Λ, plus some propagating particles. It is shown that globally synchronized period-three oscillations can be obtained if the lattice size L is a multiple of the spatial periodicity S(Λ) of the domain. When L=m.S(Λ)-1 there is a cyclic particle reaction that keeps the system in two different phases and the concentration has a temporal periodicity that depends on the lattice size. The effects of random noise on the evolved cellular automata has also been investigated.

scholarly journals Asymptotic boundedness and moment asymptotic expansion in ultradistribution spaces

2020 ◽  
pp. 21-21 ◽  
Author(s):  
Lenny Neyt ◽  
Jasson Vindas
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Formula ◽  
Dimensional Case ◽  
One Dimensional ◽  
Full Characterization ◽  
The Moment ◽  
The One ◽  
Structural Theorems

We obtain structural theorems for the so-called S-asymptotic and quasiasymptotic boundedness of ultradistributions. Using these results, we then analyze the moment asymptotic expansion (MAE), providing a full characterization of those ultradistributions satisfying this asymptotic formula in the one-dimensional case. We also introduce and study a uniform variant of the MAE.

UNCONVENTIONAL INVERTIBLE BEHAVIORS IN REVERSIBLE ONE-DIMENSIONAL CELLULAR AUTOMATA

2008 ◽  
Vol 18 (12) ◽  
pp. 3625-3632
Author(s):  
JUAN CARLOS SECK TUOH MORA ◽  
MANUEL GONZÁLEZ HERNÁNDEZ ◽  
GENARO JUÁREZ MARTÍNEZ ◽  
SERGIO V. CHAPA VERGARA ◽  
HAROLD V. McINTOSH
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Temporal Evolution ◽  
Complete Characterization ◽  
Dimensional Case ◽  
Neighborhood Size ◽  
One Dimensional ◽  
Combinatorial Properties ◽  
Reversible Cellular Automata ◽  
The One

Reversible cellular automata are discrete invertible dynamical systems determined by local interactions among their components. For the one-dimensional case, there are classical references providing a complete characterization based on combinatorial properties. Using these results and the simulation of every automaton by another with neighborhood size 2, this paper describes other types of invertible behaviors embedded in these systems different from the classical one observed in the temporal evolution. In particular, spatial reversibility and diagonal surjectivity are studied, and the generation of macrocells in the evolution space is analyzed.

On the Ordering Conditions for Self-Organizing Maps

1995 ◽  
Vol 7 (2) ◽  
pp. 284-289 ◽  
Author(s):  
Marco Budinich ◽  
John G. Taylor
Keyword(s):  
Geometric Interpretation ◽  
Dimensional Case ◽  
Feature Maps ◽  
Self Organizing Maps ◽  
One Dimensional ◽  
Higher Dimensional ◽  
The One ◽  
Ordered State ◽  
Self Organizing

We present a geometric interpretation of ordering in self-organizing feature maps. This view provides simpler proofs of Kohonen ordering theorem and of convergence to an ordered state in the one-dimensional case. At the same time it explains intuitively the origin of the problems in higher dimensional cases. Furthermore it provides a geometric view of the known characteristics of learning in self-organizing nets.

Characterization of Minimum Route MTM in One-Dimensional Multi-Hop Wireless Networks

2009 ◽  
Vol E92-A (9) ◽  
pp. 2227-2235 ◽  
Author(s):  
Kazuyuki MIYAKITA ◽  
Keisuke NAKANO ◽  
Masakazu SENGOKU ◽  
Shoji SHINODA
Keyword(s):  
Wireless Networks ◽  
One Dimensional
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