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On entropic convergence of algorithms in terms of domain partitions

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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Contributor : Anatol Slissenko <>
Submitted on : Monday, June 18, 2018 - 2:17:11 PM
Last modification on : Friday, October 4, 2019 - 1:12:51 AM
Long-term archiving on: : Wednesday, September 19, 2018 - 9:35:03 PM


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  • HAL Id : hal-01817834, version 1
  • ARXIV : 1605.01519



Anatol Slissenko. On entropic convergence of algorithms in terms of domain partitions. 2016. ⟨hal-01817834⟩



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