SOME PROPERTIES OF FIBONACCI LANGUGAES

Two particular types of Fibonacci languages $F_{a, b}^1=\{a, b, ab, bab, abbab, \cdots \}$ and $F_{a, b}^0=\{a, b, ba, bab, babba, \cdots \}$ were defined on the free monoid $X^*$ generated by the alphabet $X = \{a, b\}$. In this paper we investigate some algebraic properties of these two types of Fibonacci languages. We show that a general Fibonacci language is a homomorphical image of either $F_{a, b}^1$ or $F_{a, b}^0$. We also study the properties of Fibonacci language related to formal language theory and codes We obtained the facts that every Fibonacci word is a primitive word and for any $u \in X^+$, $u^4$ is not a subword of any words in both $F_{a, b}^1$ and $F_{a, b}^0$.