Today I had a couple of formal language lectures. The Instructor wrote a regular expression for the alphabet $\{0,1\}$ which does not include any string which includes "11" as a substring.
She wrote that regular expression: $0^*\cup 0^*1(00^*1)^*0^*$. I have nothing against that but after the lecture I tried to solve that problem on my own and came up with that expression: $0^*\cup0^*(100^*)^*0^*$.
Is that true? It appears to me that I can even get rid of $0^*$ at the end of expression and simplify as $0^*\cup0^*(100^*)^*$.
