Cellular Automata Communication Models

2010 ◽  
Vol 1 (3) ◽  
pp. 66-84 ◽  
Author(s):  
Predrag T. Tošic

In this paper, cellular automata (CA) are viewed as an abstract model for distributed computing. The author argues that the classical CA model must be modified in several important respects to become a relevant model for large-scale MAS. The paper first proposes sequential cellular automata (SCA) and formalizes deterministic and nondeterministic versions of SCA. The author then analyzes differences in possible dynamics between classical parallel CA and various SCA models. The analysis in this paper focuses on one-dimensional parallel and sequential CA with node update rules restricted to simple threshold functions, as arguably the simplest totalistic, yet non-linear (and non-affine) update rules. The author identifies properties of asymptotic dynamics that can be proven to be entirely due to the assumption of perfect synchrony in classical, parallel CA. Finally, the paper discusses what an appropriate CA-based abstraction would be for large-scale distributed computing, insofar as the inter-agent communication models. In that context, the author proposes genuinely asynchronous CA and discusses main differences between genuinely asynchronous CA and various weakly asynchronous sequential CA models found in the literature.

Author(s):  
Predrag T. Tošic

In this paper, cellular automata (CA) are viewed as an abstract model for distributed computing. The author argues that the classical CA model must be modified in several important respects to become a relevant model for large-scale MAS. The paper first proposes sequential cellular automata (SCA) and formalizes deterministic and nondeterministic versions of SCA. The author then analyzes differences in possible dynamics between classical parallel CA and various SCA models. The analysis in this paper focuses on one-dimensional parallel and sequential CA with node update rules restricted to simple threshold functions, as arguably the simplest totalistic, yet non-linear (and non-affine) update rules. The author identifies properties of asymptotic dynamics that can be proven to be entirely due to the assumption of perfect synchrony in classical, parallel CA. Finally, the paper discusses what an appropriate CA-based abstraction would be for large-scale distributed computing, insofar as the inter-agent communication models. In that context, the author proposes genuinely asynchronous CA and discusses main differences between genuinely asynchronous CA and various weakly asynchronous sequential CA models found in the literature.


2011 ◽  
Author(s):  
Βασίλειος Μαρδύρης

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.


Author(s):  
Alan Gibbons ◽  
Martyn Amos

Motivated by questions in biology and distributed computing, the authors investigate the behaviour of particular cellular automata, modelled as one-dimensional arrays of identical finite automata. They investigate what kinds of self-stabilising cooperative behaviour may be induced in terms of waves of cellular state changes along a filament of cells. The authors report the minimum requirements, in terms of numbers of states and the range of communication between automata, for this behaviour to be observed in individual filaments. They also discover that populations of growing filaments may have useful features not possessed by individual filaments, and they report the results of numerical simulations.


2010 ◽  
Vol 1 (1) ◽  
pp. 56-69
Author(s):  
Alan Gibbons ◽  
Martyn Amos

Motivated by questions in biology and distributed computing, the authors investigate the behaviour of particular cellular automata, modelled as one-dimensional arrays of identical finite automata. They investigate what kinds of self-stabilising cooperative behaviour may be induced in terms of waves of cellular state changes along a filament of cells. The authors report the minimum requirements, in terms of numbers of states and the range of communication between automata, for this behaviour to be observed in individual filaments. They also discover that populations of growing filaments may have useful features not possessed by individual filaments, and they report the results of numerical simulations.


2004 ◽  
Vol 14 (09) ◽  
pp. 3217-3248 ◽  
Author(s):  
RAMÓN ALONSO-SANZ

Standard Cellular Automata (CA) are ahistoric (memoryless): i.e. the new state of a cell depends on the neighborhood configuration only at the preceding time step. This article introduces an extension to the standard framework of CA by considering automata implementing memory capabilities. While the update rules of the CA remains the same, each site remembers a weighted mean of all its past states, with a decreasing weight of states farther in the past. The historic weighting is defined by a geometric series of coefficients based on a memory factor (α). This paper considers the time evolution of one-dimensional range-two CA with memory.


2002 ◽  
Vol 12 (01) ◽  
pp. 205-226 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
MARGARITA MARTÍN

Standard Cellular Automata (CA) are ahistoric (memoryless): i.e. the new state of a cell depends on the neighborhood configuration only at the preceding time step. This article introduces an extension to the standard framework of CA by considering automata implementing memory capabilities. While the update rules of the CA remain the same, each site remembers a weighted mean of all its past states. The historic weighting is defined by a geometric series of coefficients based on a memory factor (α). The time evolution of one-dimensional CA with memory starting with a single live cell is studied. It is found that for α ≤ 0.5, the evolution corresponds to the standard (nonweighted) one, while for α > 0.5, there is a gradual decrease in the width of the evolving pattern, apart from discontinuities which sometimes may occur for certain rules and α values.


2004 ◽  
Vol 15 (10) ◽  
pp. 1461-1470 ◽  
Author(s):  
JUAN R. SÁNCHEZ ◽  
RAMÓN ALONSO-SANZ

Standard Cellular Automata (CA) are ahistoric (memoryless Markov process), i.e., the new state of a cell depends on the neighborhood configuration only at the preceding time step. This article considers the fractal and multifractal properties of an extension to the standard framework of CA implemented by the inclusion of memory capabilities. Thus, in CA with memory, while the update rules of the CA remain unaltered, historic memory of all past iterations is retained by featuring each cell by a summary of all its past states. A study is made of the effect of historic memory on the multifractal dynamical characteristics of one-dimensional cellular automata operating under one of the most studied rules, rule 90, which is well known to display a rich complex behavior.


2003 ◽  
Vol 14 (05) ◽  
pp. 695-719 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
MARGARITA MARTÍN

Standard Cellular Automata (CA) are ahistoric (memoryless), i.e., the new state of a cell depends only on the neighborhood configuration at the preceding time step. This article introduces an extension of the standard framework of CA by considering automata implementing memory capabilities. While the update rules of the CA remains the same, each site remembers a weighted mean of all its past states, with a decreasing weight of states farther back in the past. The historic weighting is defined by a potential series of coefficients, tk, k acting as a forgetting factor. This paper considers the time evolution of one-dimensional, legal CA rules with accumulative memory.


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