While minimizing DFA’s we write 1-equivalent based on final and non final states i.e we group final states and non final states separately.
But in melay machine we don’t have final state, so we write 1-equivalent based on output produced on transitions.
If we observe the table, the states {A,B,C} on seeing input 0 goes to some other state producing output 0, similarly these states on 1 produces output 1 therefore in 1-equivalent we make A,B,C as a group.
Similarly state D on input 0 produces 1 and input 1 produces 1, and D is only state producing such output therefore we put D in another group.
{A,B,C} {D} – 1-equivalent
{A} {B,C} {D} – 2-equivalent, we found it similar to finding 2-equivalent in DFA minimization
{A} {B,C} {D} – 3-equivalent
Therefore we combine B,C states
https://www.youtube.com/watch?v=oDyz5yUFas4