Characterizing Cantorian sets by entropy-like quantities

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. © Emerald Group Publishing Limited.SCOPUS: ar.j