Institute of Informatics
Acta Cybernetica
Past Issues
Volume 15, Number 2, 2001
Sets of integers in different number systems and the Chomsky hierarchy
# Sets of integers in different number systems and the Chomsky hierarchy

**István Katsányi**

### Abstract (in LaTeX format)

The classes of the Chomsky hierarchy are characterized in respect of converting between canonical number systems. We show that the relations of the bases of the original and converted number systems fall into four distinct categories, and we examine the four Chomsky classes in each of the four cases. We also prove that all of the Chomsky classes are closed under constant addition and multiplication. The classes $\re$ and $\cs$ are closed under every examined operation. The regular languages are closed under addition, but not under multiplication.

### Full text

Available electronic editions: PDF.

### DOI

DOI is not available for this article.

### BibTeX entry
`
@article{Katsanyi:2001:ActaCybernetica,`

author = {Istv{\'a}n Kats{\'a}nyi},

title = {Sets of integers in different number systems and the Chomsky hierarchy},

journal = {Acta Cybernetica},

year = {2001},

volume = {15},

pages = {121--136},

number = {2},

abstract = {The classes of the Chomsky hierarchy are characterized in respect of converting between canonical number systems. We show that the relations of the bases of the original and converted number systems fall into four distinct categories, and we examine the four Chomsky classes in each of the four cases. We also prove that all of the Chomsky classes are closed under constant addition and multiplication. The classes $\re$ and $\cs$ are closed under every examined operation. The regular languages are closed under addition, but not under multiplication.}

}