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Preliminary Investigation of Random SKI-Combinator Trees

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Abstract

SKI-combinator trees are a simple model of computation, which are computationally complete (in a Turing sense), but are suggestive of basic biochemical processes and can be used as a vehicle for understanding processes of biological (and prebiotic) self-organization. After a brief overview of SKI-combinator trees, we describe the results of a series of preliminary experiments exploring the statistical properties of populations of random SKI-combinator trees. We show that in such populations a significant fraction of the trees will exhibit complex, non-terminating growth patterns, suggestive of biological processes. Further, we show that the fraction of S-combinators in such trees is an important parameter defining a sharp phase transition between (uninteresting) terminating behavior and (interesting) nonterminating growth. (This is related to the "edge of chaos" investigated by Chris Langton.) Finally, we discuss some of the follow-on investigations suggested by these exploratory expe...
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... Third, such a universal set might provide building blocks for the quasi-evolutionary CAM process. (Indeed, we have already begun investigating statistical properties of " soups " of ¢ 4 £ complexes, which might be used as the raw materials of the CAM process [13, 21].) Smart Matter is being developed at the Xerox Palo Alto Research Center. ...
... Therefore, we will need to develop means (both chemical and computational) for decreasing the probability of such errors, for correcting them when they occur, or for assuring that results are insensitive to them. Further, unpublished preliminary investigations indicate that a certain fraction of random ¢ ¤ £ trees will result in nonterminating, expansive, chain reactions [13, 21]. (The probability of termination decreases with increasing random tree size.) ...
... Third, such a universal set might provide building blocks for the quasi-evolutionary CAM process. (Indeed, we have already begun investigating statistical properties of "soups" of ¢ 4 £ complexes, which might be used as the raw materials of the CAM process [13,21].) ...
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... Third, such a universal set might provide building blocks for the quasi-evolutionary CAM process. (Indeed, we have already begun investigating statistical properties of " soups " of ËÃ complexes, which might be used as the raw materials of the CAM process [18][19].) Smart Matter is being developed at the Xerox Palo Alto Research Center. ...
... Therefore, we will need to develop means (both chemical and computational) for decreasing the probability of such errors, for correcting them when they occur, or for assuring that results are insensitive to them. Further , unpublished preliminary investigations indicate that a certain fraction of random ËÃ trees will result in nonterminating, expansive, chain reactions [18][19] . (The probability of termination decreases with increasing random tree size.) ...
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