How many number of DFA states exist for the transition function as given below:
Stae |
a |
b |
p |
{q, s} |
{q} |
*q |
{r} |
{q, r} |
r |
{s} |
{p} |
*s |
{p |
φ |
(A) 5
(B) 8
(C) 10
(D) 11
Answer: (C)
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 |
There are total 10 states in DFA.
So, option (C) is correct.
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