Characterizing Cantorian sets by entropy‐like quantities

Abstract

Purpose

The purpose of this paper is to discuss the recognizability of Cantorian stochastic automata by generalized entropy‐like qualities.

Design/methodology/approach

The paper gives a necessary entropy condition, valid for all sequences on the alphabet {0, 1} read by lumping and generated by a Cantorian stochastic automaton.

Findings

The paper finds that, on this basis, once can determine that a given sequence is not generated by Cantorian stochastic automata and reconstruct the automaton when the sequence is generated by a Cantorian stochastic automaton.

Originality/value

This paper derives a new diagnostic for Cantorian stochastic automata, which could find a direct application to biology, where there is a recent claim that the coding regions of chromosomes form Cantor sets.

Citation

Karamanos, K. (2009), "Characterizing Cantorian sets by entropy‐like quantities", Kybernetes, Vol. 38 No. 6, pp. 1025-1032. https://doi.org/10.1108/03684920910973234