EXAMPLE $9\mathrm{.}6$

For $=\{0,1\},$ design a Turing machine that accepts the language denoted by the regular expression ${00}^{**}.$

This is an easy exercise in Turing machine programming. Starting at the left end of the input, we read each symbol and check that it is a $0.$ If it is$,$ we continue by moving right. If we reach a blank without encountering anything but $0,$ we terminate and accept the string. If the input contains a $1$ anywhere, the string is not in $L({00}^{**}),$ and we halt in a nonfinal state. To keep track of the computation, two internal states $Q=\{q_0,q_1\}$ and one final state $F=\{q_1\}$ are sufficient. As transition function we can take

$(q_0,0)=(q_0,0,R),$

$(q_0,)=(q_1,,R).$

As long as a $0$ appears under the read$-$write head, the head will move to the right. If at any time a $1$ is read, the machine will halt in the nonfinal state $q_0,$ since $(q_0,1)$ is undefined. Note that the Turing machine also halts in a final state if started in state $q_0$ on a blank. We could interpret this as acceptance of $,$ but for technical reasons the empty string is not included in Definition $9\mathrm{.}3.$

MY QUESTION. I think the anwer is wrong. Because the given transition function could accept empty string$().$ Isn't it$?$