I have a context free grammar defined by the following rules.
S -> X .
S -> Y .
X -> 0 X .
X -> 0 A .
Y -> Y 1 .
Y -> A 1 .
A -> e (epsilon)
A -> 0 A 1 .
I know that this creates the following strings (and many more)
1
0
1 1
0 0
1 1 1
0 1 1
0 0 1
0 0 0
1 1 1 1
0 0 0 0
0 1 1 1
0 0 0 1
1 1 1 1 1
0 1 1 1 1
0 0 0 1 1
0 0 1 1 1
0 0 0 0 1
0 0 0 0 0
I think I can define this as
(0^n)(1^m) or (0^m)(1^n) where m<n
but how can I define this formally as a regular expression?