# Is this FA really equivalent to the given regular expression?

From the picture, the automata can accept $$(\text L|\text D)^*$$ following say $$\_\text L\text D$$, but in the formula above $$(\text L|\text D)^*$$ can't follow the $$\_\text L\text D$$.

So the Automata in the picture is not equivalent to the RE?

• $(L|D)^+ \equiv (L|D)(L|D)^\ast$, hence after a word in $\_(L|D)$ there can be arbitrary many words matching $(L|D)$. – ttnick Mar 17 '20 at 8:09
• @ttnick: Thank you! – Ning Mar 17 '20 at 8:11