scholarly journals Representing Reversible Cellular Automata with Reversible Block Cellular Automata

2001 ◽  
Vol DMTCS Proceedings vol. AA,... (Proceedings) ◽  
Author(s):  
Jérôme Durand-Lose
Keyword(s):  
System Theory ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Linear Time ◽  
Fixed Size ◽  
Mathematical System ◽  
Reversible Cellular Automaton ◽  
International Audience ◽  
Infinite Lattices ◽  
Reversible Cellular Automata

International audience Cellular automata are mappings over infinite lattices such that each cell is updated according tothe states around it and a unique local function.Block permutations are mappings that generalize a given permutation of blocks (finite arrays of fixed size) to a given partition of the lattice in blocks.We prove that any d-dimensional reversible cellular automaton can be exp ressed as thecomposition of d+1 block permutations.We built a simulation in linear time of reversible cellular automata by reversible block cellular automata (also known as partitioning CA and CA with the Margolus neighborhood) which is valid for both finite and infinite configurations. This proves a 1990 conjecture by Toffoli and Margolus <i>(Physica D 45)</i> improved by Kari in 1996 <i>(Mathematical System Theory 29)</i>.

scholarly journals A Novel Image Encryption Scheme Based on Reversible Cellular Automata

2019 ◽  
Vol 1 (1) ◽  
Author(s):  
AliMohammad Latif ◽  
Zeinab Mehrnahad
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Image Encryption ◽  
Experimental Results ◽  
Encryption Scheme ◽  
Encrypted Image ◽  
Reversible Cellular Automaton ◽  
Quantitative Performance ◽  
Image Pixels ◽  
Reversible Cellular Automata

In this paper, a new scheme for image encryption is presented by reversible cellular automata. The presented scheme is applied in three individual steps. Firstly, the image is blocked and the pixels are substituted by a reversible cellular automaton. Then, image pixels are scrambled by an elementary cellular automata and finally the blocks are attached and pixels are substituted by an individual reversible cellular automaton. Due to reversibility of used cellular automata, decryption scheme can reversely be applied. The experimental results show that encrypted image is suitable visually and this scheme has satisfied quantitative performance.

scholarly journals Number conserving cellular automata: new results on decidability and dynamics

2003 ◽  
Vol DMTCS Proceedings vol. AB,... (Proceedings) ◽  
Author(s):  
Bruno Durand ◽  
Enrico Formenti ◽  
Aristide Grange ◽  
Zsuzsanna Róka
Keyword(s):  
Cellular Automata ◽  
Linear Time ◽  
Number Conservation ◽  
International Audience

International audience This paper is a survey on our recent results about number conserving cellular automata. First, we prove the linear time decidability of the property of number conservation. The sequel focuses on dynamical evolutions of number conserving cellular automata.

scholarly journals Larger than Life: Digital Creatures in a Family of Two-Dimensional Cellular Automata

2001 ◽  
Vol DMTCS Proceedings vol. AA,... (Proceedings) ◽  
Author(s):  
Kellie M. Evans
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Nearest Neighbor ◽  
Two Dimensional ◽  
Game Of Life ◽  
Large Neighborhood ◽  
International Audience ◽  
Parameter Values

International audience We introduce the Larger than Life family of two-dimensional two-state cellular automata that generalize certain nearest neighbor outer totalistic cellular automaton rules to large neighborhoods. We describe linear and quadratic rescalings of John Conway's celebrated Game of Life to these large neighborhood cellular automaton rules and present corresponding generalizations of Life's famous gliders and spaceships. We show that, as is becoming well known for nearest neighbor cellular automaton rules, these ``digital creatures'' are ubiquitous for certain parameter values.

PARALLEL GENERATION AND PARSING OF ARRAY LANGUAGES USING REVERSIBLE CELLULAR AUTOMATA

1994 ◽  
Vol 08 (02) ◽  
pp. 543-561 ◽  
Author(s):  
KENICHI MORITA ◽  
SATOSHI UENO
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Reversible Cellular Automata ◽  
New System

We propose a new system of generating array languages in parallel, based on a partitioned cellular automaton (PCA), a kind of cellular automaton. This system is called a PCA array generator (PCAAG). The characteristic of PCAAG is that a”reversible” version is easily defined. A reversible PCA (RPCA) is a backward deterministic PCA, and we can construct a deterministic “inverse” PCA that undoes the operations of the RPCA. Thus if an array language is generated by an RPCA, it can be parsed in parallel by a deterministic inverse PCA without backtracking. We also define two subclasses of PCAAG, and give examples of them that generate geometrical figures.

Self-Reproduction in Three-Dimensional Reversible Cellular Space

2002 ◽  
Vol 8 (2) ◽  
pp. 155-174 ◽  
Author(s):  
Katsunobu Imai ◽  
Takahiro Hori ◽  
Kenichi Morita
Keyword(s):  
Cellular Automata ◽  
Power Dissipation ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Large Problem ◽  
Cellular Space ◽  
Reversible Cellular Automaton ◽  
Dimensional Version ◽  
Reversible Cellular Automata ◽  
Physical Phenomena

Due to inevitable power dissipation, it is said that nano-scaled computing devices should perform their computing processes in a reversible manner. This will be a large problem in constructing three-dimensional nano-scaled functional objects. Reversible cellular automata (RCA) are used for modeling physical phenomena such as power dissipation, by studying the dissipation of garbage signals. We construct a three-dimensional self-inspective self-reproducing reversible cellular automaton by extending the two-dimensional version SR8. It can self-reproduce various patterns in three-dimensional reversible cellular space without dissipating garbage signals.

scholarly journals SPECTRAL PROPERTIES OF REVERSIBLE ONE-DIMENSIONAL CELLULAR AUTOMATA

2003 ◽  
Vol 14 (03) ◽  
pp. 379-395 ◽  
Author(s):  
JUAN CARLOS SECK TUOH MORA ◽  
SERGIO V. CHAPA VERGARA ◽  
GENARO JUÁREZ MARTÍNEZ ◽  
HAROLD V. McINTOSH
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Spectral Properties ◽  
Neighborhood Size ◽  
Local Behavior ◽  
One Dimensional ◽  
Single Positive ◽  
Reversible Cellular Automata ◽  
Inverse Rule

Reversible cellular automata are invertible dynamical systems characterized by discreteness, determinism and local interaction. This article studies the local behavior of reversible one-dimensional cellular automata by means of the spectral properties of their connectivity matrices. We use the transformation of every one-dimensional cellular automaton to another of neighborhood size 2 to generalize the results exposed in this paper. In particular we prove that the connectivity matrices have a single positive eigenvalue equal to 1; based on this result we also prove the idempotent behavior of these matrices. The significance of this property lies in the implementation of a matrix technique for detecting whether a one-dimensional cellular automaton is reversible or not. In particular, we present a procedure using the eigenvectors of these matrices to find the inverse rule of a given reversible one-dimensional cellular automaton. Finally illustrative examples are provided.

scholarly journals Periodic Patterns in Orbits of Certain Linear Cellular Automata

2001 ◽  
Vol DMTCS Proceedings vol. AA,... (Proceedings) ◽  
Author(s):  
André Barbé ◽  
Fritz Haeseler
Keyword(s):  
Cellular Automata ◽  
Finite Field ◽  
Cellular Automaton ◽  
Periodic Patterns ◽  
Periodic Behavior ◽  
Universal Behavior ◽  
International Audience

International audience We discuss certain linear cellular automata whose cells take values in a finite field. We investigate the periodic behavior of the verticals of an orbit of the cellular automaton and establish that there exists, depending on the characteristic of the field, a universal behavior for the evolution of periodic verticals.

scholarly journals The reversibility of one-dimensional cellular automata

2021 ◽  
Vol 22 (1) ◽  
pp. 7-15
Author(s):  
Alexey E. Zhukov
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
High Performance ◽  
Finite Automata ◽  
Finite Size ◽  
Transition Function ◽  
One Dimensional ◽  
Enumeration Problems ◽  
Reversible Cellular Automata ◽  
Binary Filter

Recently the reversible cellular automata are increasingly used to build high-performance cryptographic algorithms. The paper establishes a connection between the reversibility of homogeneous one-dimensional binary cellular automata of a finite size and the properties of a structure called binary filter with input memory and such finite automata properties as the prohibitions in automata output and loss of information. We show that finding the preimage for an arbitrary configuration of a one-dimensional cellular automaton of length L with a local transition function f is associated with reversibility of a binary filter with input memory. As a fact, the nonlinear filter with an input memory corresponding to our cellular automaton does not depend on the number of memory cells of the cellular automaton. The results obtained make it possible to reduce the complexity of solving massive enumeration problems related to the issues of reversibility of cellular automata. All the results obtained can be transferred to cellular automata with non-binary cell filling and to cellular automata of dimension greater than 1.

Clustering Using Cyclic Spaces of Reversible Cellular Automata

2021 ◽  
Vol 30 (2) ◽  
pp. 205-237
Author(s):  
Sukanya Mukherjee ◽  
◽  
Kamalika Bhattacharjee ◽  
Sukanta Das ◽  
◽  
...  
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Configuration Space ◽  
Present Level ◽  
Number Of Clusters ◽  
Clustering Techniques ◽  
Clustering Technique ◽  
Previous Level ◽  
Reversible Cellular Automata ◽  
Number Of Cycles

This paper introduces a cycle-based clustering technique using the cyclic spaces of reversible cellular automata (CAs). Traditionally, a cluster consists of close objects, which in the case of CAs necessarily means that the objects belong to the same cycle; that is, they are reachable from each other. Each of the cyclic spaces of a cellular automaton (CA) forms a unique cluster. This paper identifies CA properties based on “reachability” that make the clustering effective. To do that, we first figure out which CA rules contribute to maintaining the minimum intracluster distance. Our CA is then designed with such rules to ensure that a limited number of cycles exist in the configuration space. An iterative strategy is also introduced that can generate a desired number of clusters by merging objects of closely reachable clusters from a previous level in the present level using a unique auxiliary CA. Finally, the performance of our algorithm is measured using some standard benchmark validation indices and compared with existing well-known clustering techniques. It is found that our algorithm is at least on a par with the best algorithms existing today on the metric of these standard validation indices.

Simulating Self-Regeneration and Self-Replication Processes Using Movable Cellular Automata with a Mutual Equilibrium Neighborhood

2020 ◽  
Vol 29 (4) ◽  
pp. 741-757
Author(s):  
Kateryna Hazdiuk ◽  
◽  
Volodymyr Zhikharevich ◽  
Serhiy Ostapov ◽  
◽  
...  
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Three Dimensional ◽  
Computer Models ◽  
The Self ◽  
Model Construction ◽  
Natural Phenomena ◽  
Different Types ◽  
Movable Cellular Automata ◽  
Self Replication

This paper deals with the issue of model construction of the self-regeneration and self-replication processes using movable cellular automata (MCAs). The rules of cellular automaton (CA) interactions are found according to the concept of equilibrium neighborhood. The method is implemented by establishing these rules between different types of cellular automata (CAs). Several models for two- and three-dimensional cases are described, which depict both stable and unstable structures. As a result, computer models imitating such natural phenomena as self-replication and self-regeneration are obtained and graphically presented.

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