The Sum 2 KM(x)−K(x) Over All Prefixes x of Some Binary Sequence Can be Infinite
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چکیده
منابع مشابه
The sum $2^{\mathit{KA}(x)-\mathit{KP}(x)}$ over all prefixes $x$ of some binary sequence can be infinite
We consider two quantities that measure complexity of binary strings: KM(x) is defined as the minus logarithm of continuous a priori probability on the binary tree, and K(x) denotes prefix complexity of a binary string x. In this paper we answer a question posed by Joseph Miller and prove that there exists an infinite binary sequence ω such that the sum of 2KM(x)−K(x) over all prefixes x of ω i...
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ژورنال
عنوان ژورنال: Theory of Computing Systems
سال: 2015
ISSN: 1432-4350,1433-0490
DOI: 10.1007/s00224-014-9604-2