I want to prove that $L = \{\langle T\rangle\mid T \text{ is a DFA and $L(T)$=$(101)^*$}\}$ is decidable.I have the following idea in mind: I design a TM $M$ such that, first of all, $M$ converts $(101)^*$ to NFA $P$. Then it converts $P$ to DFA $K$. After that $M$ determines whether $K$ and $T$ recognise the same language using the fact that $EQ = \{\langle A,B\rangle\mid A,B \text{ are DFAs and $L(A)=L(B)$}\}$ is decidable.Is the solution idea correct? If not, then what would be the best way to solve the problem?
Deciding the language of DFAs accepting $(101)^*$
computability;turing machines;regular languages