I am trying to find a generating for the number of binary string with the property that every block of $0$'s of length $ \ge 4$ is followed by a block of $1$'s of length $\ge 4$. I got the following decomposition but my professor says it is wrong. Can somebody tell me why it is wrong and how I can correct it? Thank
$1^*\{01^*,0^21^*,0^31^*,0^40^*1^41^*\}^*$