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Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

Good paper on approximation and error size issues in CA modeling

There was a paper in originally made available online in 2004 that only recently came to my attention, by a researcher in Russia named Olga Bandman (Russian Academy of Sciences), that I thought some others here might find useful.

It is of interest for the data fitting or backward problem, of figuring out what CA might have produced given spatial data. In general in such problems there is "play" in, effectively, scaling parameters or coefficients, that "trade off" with assumptions about how coarsely the observations "aggregate" behavior in a postulated, underlying CA driver.

The paper is "Computation properties of spatial dynamics simulation by probabilistic cellular automata", and it appeared in the journal Future Generation Computer Systems, Volume 21, issue 5, pages 633-634. It is published by Elsevier, with ISSN/ISBN identifier 0167-739X.

Here is the abstract -

Accuracy, stability and computation complexity of fine-grained parallel simulation of spatial dynamics by probabilistic cellular automata (CA), are assessed and experimentally studied. Under investigation are probabilistic CA constructed as a composition of an ordinary CA with a function given in real numbers. The accuracy problem is reduced to approximation error assessment of the transformation of a real spatial function into a Boolean array and addition of cellular arrays with different cell state alphabets: real and Boolean. Some techniques for determining simulation parameters which provide a given accuracy are given. Stability is shown to be dependent only on real function, the CA component of the dynamics having no effect on it. Computation complexity of simulation process is also assessed. Some experimental results supporting the theoretical conclusions are presented.

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