The statistical properties of one-dimensional strings of symbols are investigated. For this purpose several measures of complexity are applied to a DNA sequence and various reference strings as Markov chains, chaotic sequences and languages. With respect to Shannon entropies of words the DNA strings is comparable to Markov chains. However, the long-range correlations detected by mutual information remind more to the statistical properties of a computer language. This similarity to languages is confirmed by another powerful statistical approach: the analysis of Hamming distances between words. Moreover, stochastic evolutionary games are discussed which might be related to the complexity of biomolecules. It is argued that an appropriate compromise between sharp selection and variability can result from chaotic dynamics or frustrated rules.
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Ebeling et al. (1987) studied this question.
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