3,037 research outputs found
Transfer matrix analysis of one-dimensional majority cellular automata with thermal noise
Thermal noise in a cellular automaton refers to a random perturbation to its
function which eventually leads this automaton to an equilibrium state
controlled by a temperature parameter. We study the 1-dimensional majority-3
cellular automaton under this model of noise. Without noise, each cell in this
automaton decides its next state by majority voting among itself and its left
and right neighbour cells. Transfer matrix analysis shows that the automaton
always reaches a state in which every cell is in one of its two states with
probability 1/2 and thus cannot remember even one bit of information. Numerical
experiments, however, support the possibility of reliable computation for a
long but finite time.Comment: 12 pages, 4 figure
Making Classical Ground State Spin Computing Fault-Tolerant
We examine a model of classical deterministic computing in which the ground
state of the classical system is a spatial history of the computation. This
model is relevant to quantum dot cellular automata as well as to recent
universal adiabatic quantum computing constructions. In its most primitive
form, systems constructed in this model cannot compute in an error free manner
when working at non-zero temperature. However, by exploiting a mapping between
the partition function for this model and probabilistic classical circuits we
are able to show that it is possible to make this model effectively error free.
We achieve this by using techniques in fault-tolerant classical computing and
the result is that the system can compute effectively error free if the
temperature is below a critical temperature. We further link this model to
computational complexity and show that a certain problem concerning finite
temperature classical spin systems is complete for the complexity class
Merlin-Arthur. This provides an interesting connection between the physical
behavior of certain many-body spin systems and computational complexity.Comment: 24 pages, 1 figur
Identification of the transition rule in a modified cellular automata model: the case of dendritic NH4Br crystal growth
A method of identifying the transition rule, encapsulated in a modified cellular automata (CA) model, is demonstrated using experimentally observed evolution of dendritic crystal growth patterns in NH4Br crystals. The influence of the factors, such as experimental set-up and image pre-processing, colour and size calibrations, on the method of identification are discussed in detail. A noise reduction parameter and the diffusion velocity of the crystal boundary are also considered. The results show that the proposed method can in principle provide a good representation of the dendritic growth anisotropy of any system
Cellular Automata
Modelling and simulation are disciplines of major importance for science and engineering. There is no science without models, and simulation has nowadays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The main attractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has attracted the researchers' attention from a wide variety of divergent fields of the exact disciplines of science and engineering, but also of the social sciences, and sometimes beyond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very different purposes. In this book, a number of innovative applications of cellular automata models in the fields of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented
Electron Spin for Classical Information Processing: A Brief Survey of Spin-Based Logic Devices, Gates and Circuits
In electronics, information has been traditionally stored, processed and
communicated using an electron's charge. This paradigm is increasingly turning
out to be energy-inefficient, because movement of charge within an
information-processing device invariably causes current flow and an associated
dissipation. Replacing charge with the "spin" of an electron to encode
information may eliminate much of this dissipation and lead to more
energy-efficient "green electronics". This realization has spurred significant
research in spintronic devices and circuits where spin either directly acts as
the physical variable for hosting information or augments the role of charge.
In this review article, we discuss and elucidate some of these ideas, and
highlight their strengths and weaknesses. Many of them can potentially reduce
energy dissipation significantly, but unfortunately are error-prone and
unreliable. Moreover, there are serious obstacles to their technological
implementation that may be difficult to overcome in the near term.
This review addresses three constructs: (1) single devices or binary switches
that can be constituents of Boolean logic gates for digital information
processing, (2) complete gates that are capable of performing specific Boolean
logic operations, and (3) combinational circuits or architectures (equivalent
to many gates working in unison) that are capable of performing universal
computation.Comment: Topical Revie
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