B) Option is not Correct answer! for this transition graph.
In Transition Graph(TG) symbol ε
means NULL-move (ε-move
). There is two NULL-moves in TG.
One: (A) --- `ε` ---->(B)
Second: (A) --- `ε` ---->(C)
A ε-move
means without consume any symbol you can change state. In your diagram from A to B
, or A to C
.
What will be δ(A,01) equal to ?
Question asked "what is path from state A
if input is 01
". (as I understand because there is only one final state)
01
can be processed in either of two ways.
(A) -- ε --->(B) -- 0 --> (B) -- 1 --> (D)
(A) -- ε --->(C) -- 0 --> (B) -- 1 --> (D)
Also, there is no other way to process string 01
even if you don't wants to reach final state.
[ANSWER]
So there is misprinting in question (or either you did).
You can learn how to remove NULL-move from transition graph. Also HOW TO WRITE REGULAR EXPRESSION FOR A DFA
If you remove null-moves from TG you will get three ways to accept 01
.
EQUIVALENT TRANSITION GRAPH WITHOUT NULL-MOVE
Note there is three start-states in Graph.
Three ways:
{ABD}
{CBD}
{BBD}
In all option state-(B)
has to be come.
Also, you have written Consider the DFA :
is wrong. The TG is not deterministic because there is there is non-deterministic move δ(A,ε) and next states are either B or C.