Institute of Informatics
Acta Cybernetica
Past Issues
Volume 15, Number 3, 2002
Factorizations of Languages and Commutativity Conditions
# Factorizations of Languages and Commutativity Conditions

**Alexandru Mateescu,
Arto Salomaa,
and Sheng Yu**

### Abstract (in LaTeX format)

Representations of languages as a product (catenation) of languages are investigated, where the factor languages are ``prime'', that is, cannot be decomposed further in a nontrivial manner. In general, such prime decompositions do not necessarily exist. If they exist, they are not necessarily unique - the number of factors can vary even exponentially. The paper investigates prime decompositions, as well as the commuting of the factors, especially for the case of finite languages. In particular, a technique about commuting is developed in Section 4, where the factorization of languages $L_1$ and $L_2$ is discussed under the assumption $L_1L_2=L_2L_1.$

**Keywords: ** finite language, catenation, commutativity of languages, prime decomposition.

### Full text

Available electronic editions: PDF.

### DOI

DOI is not available for this article.

### BibTeX entry
`
@article{Mateescu:2002:ActaCybernetica,`

author = {Alexandru Mateescu and Arto Salomaa and Sheng Yu},

title = {Factorizations of Languages and Commutativity Conditions},

journal = {Acta Cybernetica},

year = {2002},

volume = {15},

pages = {339--351},

number = {3},

abstract = {Representations of languages as a product (catenation) of languages are investigated, where the factor languages are ``prime'', that is, cannot be decomposed further in a nontrivial manner. In general, such prime decompositions do not necessarily exist. If they exist, they are not necessarily unique - the number of factors can vary even exponentially. The paper investigates prime decompositions, as well as the commuting of the factors, especially for the case of finite languages. In particular, a technique about commuting is developed in Section 4, where the factorization of languages $L_1$ and $L_2$ is discussed under the assumption $L_1L_2=L_2L_1.$},

keywords = {finite language, catenation, commutativity of languages, prime decomposition}

}