Prove or disprove that the following language is decidable: \[ \begin{align*} L_{HELLO} = \{\langle H \rangle : &\text{ $H$ is a Turing machine that prints ``HELLO''}\\ &\text{somewhere on its first tape when run with an empty input tape}\} \end{align*} \]
Prove or disprove the following language is decidable: \[ E_{DFA} = \{\langle M \rangle : M \text{ is a DFA accepting the language } \varnothing \} \] Hint: Try an approach that doesn’t involve a reduction.
Prove or disprove the following language is decidable: \[ EQ_{DFA} = \{\langle M_1, M_2 \rangle : M_1 \text{ and $M_2$ are DFAs accepting the same language} \} \]
Hint: Try reducing this to \(E_{DFA}\) from #2.
(Bonus) Prove or disprove the following language is decidable: \[ EQ_{TM} = \{\langle M_1, M_2 \rangle : M_1 \text{ and $M_2$ are turing machines accepting the same language} \} \]