Convert to a DFA for the following NFA:

Stae	0	1
p	{q, s}	{q}
*q	{r}	{q, r}
r	{s}	{p}
*s	φ	{p}

Where, p is the starting state,
Both q ans s are final states.

Which of the following option is correct regarding DFA of above transition functions?
(A) There are 7 final states and 3 non-final states in DFA
(B) There are 6 final states and 6 non-final states in DFA
(C) There are 5 final states and 5 non-final states in DFA
(D) There are 5 final states and 3 non-final states in DFA


Answer: (A)

Explanation: The table for the equivalent DFA using the subset construction is:

State	a	b
{p}	{q, s}	{q}
*{q, s}	{r}	{p,q ,r}
*{q}	{r}	{q, r}
{r}	{s}	{p}
*{p, q, r}	{q, r, s}	{p, q, r}
*{q, r}	{r, s}	{p, q, r}
*{s}	φ	{p}
*{q, r, s}	{r, s}	{p, q, r}
*{r, s}	{s}	{p}
φ	φ	φ

Where, {p} is the starting state,
State {q, s}, {q}, {p, q, r}, {q, r}, {s}, {q, r, s}, {r, s} are final states.

There are total 10 states in DFA, in which 7 states are final and 3 states are non-final.

So, option (A) is correct.

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