scholarly journals Product decomposition for surjective 2-block NCCA

2011 ◽  
Vol DMTCS Proceedings vol. AP,... (Proceedings) ◽  
Author(s):  
Felipe García-Ramos
Keyword(s):  
Cellular Automata ◽  
Product Decomposition ◽  
One Dimensional ◽  
International Audience

International audience In this paper we define products of one-dimensional Number Conserving Cellular Automata (NCCA) and show that surjective NCCA with 2 blocks (i.e radius 1/2) can always be represented as products of shifts and identites. In particular, this shows that surjective 2-block NCCA are injective.

scholarly journals Conservation Laws and Invariant Measures in Surjective Cellular Automata

2011 ◽  
Vol DMTCS Proceedings vol. AP,... (Proceedings) ◽  
Author(s):  
Jarkko Kari ◽  
Siamak Taati
Keyword(s):  
Cellular Automata ◽  
Conservation Laws ◽  
Arbitrary Dimension ◽  
Close Link ◽  
One Dimensional ◽  
Full Support ◽  
Markov Measure ◽  
Bernoulli Measure ◽  
International Audience ◽  
Markov Measures

International audience We discuss a close link between two seemingly different topics studied in the cellular automata literature: additive conservation laws and invariant probability measures. We provide an elementary proof of a simple correspondence between invariant full-support Bernoulli measures and interaction-free conserved quantities in the case of one-dimensional surjective cellular automata. We also discuss a generalization of this fact to Markov measures and higher-range conservation laws in arbitrary dimension. As a corollary, we show that the uniform Bernoulli measure is the only shift-invariant, full-support Markov measure that is invariant under a strongly transitive cellular automaton.

The dynamics of defect ensembles in one-dimensional cellular automata

1994 ◽  
Vol 76 (5-6) ◽  
pp. 1377-1398 ◽  
Author(s):  
Kari Eloranta
Keyword(s):  
Cellular Automata ◽  
One Dimensional

scholarly journals Random sampling of lattice paths with constraints, via transportation

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Lucas Gerin
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Random Sampling ◽  
Optimal Transport ◽  
Lattice Paths ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Contraction Property ◽  
International Audience

International audience We build and analyze in this paper Markov chains for the random sampling of some one-dimensional lattice paths with constraints, for various constraints. These chains are easy to implement, and sample an "almost" uniform path of length $n$ in $n^{3+\epsilon}$ steps. This bound makes use of a certain $\textit{contraction property}$ of the Markov chain, and is proved with an approach inspired by optimal transport.

scholarly journals Σχεδιασμός και προσομοίωση νανοηλεκτρικών κυκλωμάτων κβαντικών κυψελιδωτών αυτομάτων

2011 ◽  
Author(s):  
Βασίλειος Μαρδύρης
Keyword(s):  
Cellular Automata ◽  
Design Methodology ◽  
Large Scale ◽  
Modular Design ◽  
Emerging Technologies ◽  
Cmos Technology ◽  
One Dimensional ◽  
Nanoelectronic Circuits ◽  
Qca Circuits ◽  
First Time

In last decades exponential reduction of integrated circuits feature size and increase in operating frequency was achieved in VLSI fabrication industry using the conventional CMOS technology. However the CMOS technology faces serious challenges as the CMOS transistor reaches its physical limits, such as ultra thin gate oxides, short channel effects, doping fluctuations and increased difficulty and consequently increased lithography cost in the nanometer scale. It is projected that the CMOS technology, in its present state will reach its limits when the transistors channel length reaches approximatly 7 nm, probably near 2019. Emerging technologies have been a topic of great interest in the last few years. The emerging technologies in nanoelectronics provide new computing possibilities that arise from their extremely reduced feature sizes. Quantum Cellular Automata (QCA) is one of the most promising emerging technologies in the fast growing area of nanoelectronics. QCA relies mostly on Coulombic interactions and uses innovative processing techniques which are very different from the CMOS-based model. QCAs are not only a new nanoelectronic model but also provide a new method of computation and information process. In QCA circuits computation and data transfer occurs simultaneously. Appling the QCA technology, the elementary building component (QCA cells) cover an area of a few nanometers. For this feature sizes the integration can reach values of 1012 cells/cm2 and the circuit switching frequency the THz level. The implementation of digital logic using QCA nanoelectronic circuits not only drives the already developed systems based on conventional technology to the nanoelectronic era but improves their performance significantly. At the present Ph.D. thesis, a study of QCA circuit clocking schemes is presented showing how these schemes contribute to the robustness of QCA circuits. A novel design of a QCA 2 to 1 multiplexer is presented. The QCA circuit is simulated and its operation is analyzed. A modular design and simulation methodology is developed for the first time. This methodology can be used to design 2n to 1 QCA multiplexers using the 2 to 1 QCA multiplexer as a building block. The design methodology is formulated in order to increase the circuit stability.Furthermore in this Ph.D. thesis, a novel design of a small size, modular quantum-dot cellular automata (QCA) 2n to 1 multiplexer is proposed, These multiplexers can be used for memory addressing. The design objective is to develop an evolving modular design methodology which can produce QCA 2n to 1 multiplexer circuits, improved in terms of circuit area and operating frequency. In these implementations the circuit stability was a major issue and was considered carefully. In the recent years, Cellular Automata (CAs) have been widely used in order to model and simulate physical systems and also to solve scientific problems. CAs have also been successfully used as a VLSI architecture and proved to be very efficient in terms of silicon-area utilization and clock-speed maximization. In the present Ph.D. thesis a design methodology is developed for the first time, which can be used to design CA models using QCA circuitry. The implementation of CAs using QCA nanoelectronic circuits significantly improves their performance due to the unique properties of the nanoelectronic circuits. In this Ph.D. thesis a new CAD system we develope for the first time, and was named Design Automation Tool of 1-D Cellular Automata using Quantum Cellular Automata (DATICAQ), that builds a bridge between one-dimensional CAs as models of physical systems and processes and one-dimensional CAs as a nanoelectronic architecture. The CAD system inputs are the CA dimensionality, size, local rule, and the initial and boundary conditions imposed by the particular problem. DATICAQ produces as output the layout of the QCA implementation of the particular one-dimensional CA model. The proposed system also provides the simulation input vectors and their corresponding outputs, in order to simplify the simulation process. No prior knowledge of QCA circuit designing is required by the user. DATICAQ has been tested for a large number of QCA circuits. Paradigms of QCA circuits implementing CA models for zero and periodic boundary conditions are presented in the thesis. Simulations of CA models and the corresponding QCA circuits showed that the CA rules and models have been successfully implemented. At the present Ph.D. thesis, the design of large scale QCA circuits is analyzed and a study of the problems arising on complex algorithm implementation using QCAs is presented. One of the most important problems of the large scale QCA circuits is the synchronization of the internal signals of the circuit between the subsystems of the large QCA circuit. This problem becomes more difficult when the circuit includes signal loops. In the present thesis a methodology and a QCA circuit is presented for the first time, which solves the above mentioned synchronization problem. The QCA circuit implements the Firing Squad Synchronization Algorithm proposed by Mazoyer in order to solve the synchronization problem. The implementation was obtained using a one-dimensional 3-bit digital CA model. The QCA circuit is simulated and its operation is analyzed.

scholarly journals BLOCK CIPHERS ON THE BASIS OF REVERSIBLE CELLULAR AUTOMATA

2020 ◽  
Vol 10 (1) ◽  
pp. 8-11
Author(s):  
Yuliya Tanasyuk ◽  
Petro Burdeinyi
Keyword(s):  
Cellular Automata ◽  
Block Cipher ◽  
Key Generation ◽  
One Dimensional ◽  
C Programming Language ◽  
C Programming ◽  
Shared Secret ◽  
Reversible Cellular Automata ◽  
The Given ◽  
First Time

The given paper is devoted to the software development of block cipher based on reversible one-dimensional cellular automata and the study of its statistical properties. The software implementation of the proposed encryption algorithm is performed in C# programming language in Visual Studio 2017. The paper presents specially designed approach for key generation. To ensure desired cryptographic stability, the shared secret parameters can be adjusted to contain information needed for creating substitution tables, defining reversible rules, and hiding final data. For the first time, it is suggested to create substitution tables based on iterations of a cellular automaton that is initialized by the key data.

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