SOME ALGEBRAIC PROPERTIES OF SEMICODES

Let $X^{*} $ be the free monoid generated by a finite alphabet $X$, where $|X|\geq 2 $. Every element of $X^{*} $ is called a word and every subset of $X^{*} $ is called a language. The empty word is denoted by 1 and let $X^{+}=X^{*}\backslash \{1\} $. For any languages $A $ and $B $ the catenation of $A $ and $B $ is the set $AB=\{xy|x\in A, y\in B\} $ and $A^{+} $ is the set $A^{+}=A\cup A^{2}\cup A^{3}\cup\cdots