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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  • Last Updated : 13 Dec, 2018

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