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\iteman{io-port 02162119}
\itemau{Mateescu, Alexandru; Salomaa, Arto; Yu, Sheng}
\itemti{Factorizations of languages and commutativity conditions.}
\itemso{Acta Cybern. 15, No. 3, 339-351 (2002).}
\itemab
Summary: 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 $L_1 L_2= L_2 L_1$.
\itemrv{~}
\itemcc{}
\itemut{finite language; catenation; commutativity of languages; prime decomposition}
\itemli{}
\end