Anatol Slissenko | Searcharxiv

arXiv2022

Relating Information and Proof

In mathematics information is a number that measures uncertainty (entropy) based on a probabilistic distribution, often of an obscure origin. In real life language information is a datum, a statement, more precisely, a formula. But such a formula should be justified by a proof. I try to formalize this perception of information. The measure of informativeness of a proof is based on the set of proofs related to the formulas under consideration. This set of possible proofs (`a knowledge base') defines a probabilistic measure, and entropic weight is defined using this measure. The paper is mainly conceptual, it is not clear where and how this approach can be applied.

cs.AI↗

arXiv2016

On entropic convergence of algorithms in terms of domain partitions

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.

cs.CC↗