I am trying to prove the following statement:
If $S$ and $T$ are any regular expressions over a 1-letter alphabet and if $n$ is a natural, then the languages $(ST)^n$ and $S^nT^n$ are equal.
Hint: Show that any two regexps over a $1$-letter alphabet commute, i.e. $PQ = QP$ for every two regexps $P,Q$.
Hint to the hint: Show that any two words over a $1$-letter alphabet commute, i.e. $ab = ba$ for every two words $a,b$.
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
5 years ago
4 years ago
Get the weekly newsletter! In it, you'll get:
see an example newsletter