Open AccessDense Languages and Non Primitive Words
Author(s) -
Toshihiro Koga
Publication year - 2022
Publication title -
acta cybernetica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.143
H-Index - 18
eISSN - 2676-993X
pISSN - 0324-721X
DOI - 10.14232/actacyb.293457
Subject(s) - substring , generalization , string (physics) , class (philosophy) , element (criminal law) , natural density , computer science , mathematics , discrete mathematics , artificial intelligence , data structure , programming language , mathematical analysis , political science , law , mathematical physics
In this paper, we are concerned with dense languages and non primitive words. A language L is said to be dense if any string can be found as a substring of element of L. In 2020, Ryoma Syn'ya proved that any regular language with positive asymptotic density always containsinfinitely many non-primitive words. Since positive asymptotic density implies density, it is natural to ask whether his result can be generalized for a wider class of dense languages. In this paper, we actually obtain such generalization.