Question

Find a dfa that accept the following language

L((aa∗)∗ + abb)

Answer 1

checked box shows the accept state.

there are 2 kinds of string that DFA should accept since + sign indicates OR function
String 1 (aa*)*
String 2 abb

for string 1 there can be 0 or more ocurrences of (aa*)

* mean 0 or more occurrence
that means strings can be
empty string
aa
aaaaaaa

for String 2
String should be abb only.

so for 0 occurrence of a i.e. empty string, Start state itself is the accept state.

for for single occurrence of a but 0 occurence of aa* accept state is state S0
for multiple occurence of (aa*) accept state is state S1.

and for Sttring abb accept state is S2.