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Pseudorandom number generation with self programmable cellular automata
In this paper, we propose a new class of cellular automata – self programming cellular automata (SPCA) with specific application to pseudorandom number generation. By changing a cell's state transition rules in relation to factors such as its neighboring cell's states, behavioral complexity can be increased and utilized. Interplay between the state transition neighborhood and rule selection neighborhood leads to a new composite neighborhood and state transition rule that is the linear combination of two different mappings with different temporal dependencies. It is proved that when the transitional matrices for both the state transition and rule selection neighborhood are non-singular, SPCA will not exhibit non-group behavior. Good performance can be obtained using simple neighborhoods with certain CA length, transition rules etc. Certain configurations of SPCA pass all DIEHARD and ENT tests with an implementation cost lower than current reported work. Output sampling methods are also suggested to improve output efficiency by sampling the outputs of the new rule selection neighborhoods
5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal
We study two-dimensional rotation-symmetric number-conserving cellular
automata working on the von Neumann neighborhood (RNCA). It is known that such
automata with 4 states or less are trivial, so we investigate the possible
rules with 5 states. We give a full characterization of these automata and show
that they cannot be strongly Turing universal. However, we give example of
constructions that allow to embed some boolean circuit elements in a 5-states
RNCA
A New Class of Cellular Automata for Reaction-Diffusion Systems
We introduce a new class of cellular automata to model reaction-diffusion
systems in a quantitatively correct way. The construction of the CA from the
reaction-diffusion equation relies on a moving average procedure to implement
diffusion, and a probabilistic table-lookup for the reactive part. The
applicability of the new CA is demonstrated using the Ginzburg-Landau equation.Comment: 4 pages, RevTeX 3.0 , 3 Figures 214972 bytes tar, compressed,
uuencode
Phase Space Invertible Asynchronous Cellular Automata
While for synchronous deterministic cellular automata there is an accepted
definition of reversibility, the situation is less clear for asynchronous
cellular automata. We first discuss a few possibilities and then investigate
what we call phase space invertible asynchronous cellular automata in more
detail. We will show that for each Turing machine there is such a cellular
automaton simulating it, and that it is decidable whether an asynchronous
cellular automaton has this property or not, even in higher dimensions.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
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