Factorizations of Languages and Commutativity Conditions
Alexandru Mateescu, Arto Salomaa, and Sheng Yu
Acta Cybernetica 15 (2002) 339--351.
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.
Keywords:finite language, catenation, commutativity of languages, prime decomposition