Draw a DFA for the language accepting strings starting with ‘101’ over input alphabets ∑ = {0, 1}.

Solution-

Regular expression for the given language = 101(0 + 1)*

·         All strings of the language start with the substring “101”.

·         So, length of substring = 3.

Thus, Minimum number of states required in the DFA = 3 + 2 = 5.

It suggests that minimized DFA will have 5 states.

We will construct DFA for the following strings-

• 101

• 1011

• 10110

• 101101

The required DFA is-