Kolmogorov Complexity for Possibly Infinite Computations
نویسندگان
چکیده
منابع مشابه
Kolmogorov Complexity for Possibly Infinite Computations
In this paper we study the Kolmogorov complexity for non-effective computations, that is, either halting or non-halting computations on Turing machines. This complexity function is defined as the length of the shortest inputs that produce a desired output via a possibly non-halting computation. Clearly this function gives a lower bound of the classical Kolmogorov complexity. In particular, if t...
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We define a program size complexity function H∞ as a variant of the prefix-free Kolmogorov complexity, based on Turing monotone machines performing possibly unending computations. We consider definitions of randomness and triviality for sequences in {0, 1} relative to the H∞ complexity. We prove that the classes of Martin-Löf random sequences and H∞-random sequences coincide, and that the H∞-tr...
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In the context of possibly infinite computations yielding finite or infinite (binary) outputs, the space 2≤ω = 2∗∪2ω appears to be one of the most fundamental spaces in Computer Science. Though underconsidered, next to 2, this space can be viewed (§3.5.2) as the simplest compact space native to computer science. In this paper we study some of its properties involving topology and computability....
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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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Using possibly infinite computations on universal monotone Turing machines, we prove Martin-Löf randomness in ∅′ of the probability that the output be in some set O ⊆ 2≤ω under complexity assumptions about O. 1 Randomness in the spirit of Rice’s theorem for computability Let 2∗ be the set of all finite strings in the binary alphabet 2 = {0, 1}. Let 2ω be the set of all infinite binary sequences...
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ژورنال
عنوان ژورنال: Journal of Logic, Language and Information
سال: 2005
ISSN: 0925-8531,1572-9583
DOI: 10.1007/s10849-005-2255-6