Lexicographic Order of Expression [Automata Theory]
The lexicographic order is defined on words, not on regular expressions. An interesting exercise is to describe the restriction of the lexicographic order to the language $a^*b^*$, assuming that $a &lt; b$. Note for instance that
$1 &lt; a &lt; a^2 &lt; \dotsm &lt; a^n &lt; \dotsm$, but $\dotsm &lt;a^nb &lt;\dotsm &lt;a^2b &lt; ab &lt; b$.