On entropic convergence of algorithms in terms of domain partitions

Anatol Slissenko

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arXiv · 1605.01519

On entropic convergence of algorithms in terms of domain partitions

Anatol Slissenko

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Abstract

The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the viewpoint of information transformation, with a hope to better understand the work of algorithm, and maybe its complexity. The entropy is a measure of uncertainty, it does not correspond to our intuitive understanding of information. However, it is what we have in this area. In order to realize this approach we introduce a measure on the inputs of a given length based on the Principle of Maximal Uncertainty: all results should be equiprobable to the algorithm at the beginning. An algorithm is viewed as a set of events, each event is an application of a command. The commands are very basic. To measure the convergence we introduce a measure that is called entropic weight of events of the algorithm. The approach is illustrated by two examples.

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Anatol Slissenko. 2016-05-05. On entropic convergence of algorithms in terms of domain partitions. https://arxiv.org/abs/1605.01519

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