The Kolmogorov complexity of infinite words
نویسندگان
چکیده
منابع مشابه
The Kolmogorov complexity of infinite words
We present a brief survey of results on relations between the Kolmogorov complexity of infinite strings and several measures of information content (dimensions) known from dimension theory, information theory or fractal geometry. Special emphasis is laid on bounds on the complexity of strings in constructively given subsets of the Cantor space. Finally, we compare the Kolmogorov complexity to t...
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The Kolmogorov complexity function of an infinite word ξ maps a natural number to the complexity K(ξ n) of the n-length prefix of ξ. We investigate the maximally achievable complexity function if ξ is taken from a constructively describable set of infinite words. Here we are interested in linear upper bounds where the slope is the Hausdorff dimension of the set. As sets we consider Π1-definable...
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This paper contains answers to several problems in the theory of the computational complexity of infinite words. We show that the problem whether all infinite words generated by iterating dgsm’s have logarithmic space complexity is equivalent to the open problem asking whether the unary classes of languages in P and in DLOG are equivalent. Similarly, the problem to find a concrete infinite word...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2007
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2007.04.013