Create a DFA that proves $a^*b^*$ is a regular language.

Question

Can someone explain to me what "*" means? Does it mean that the language starts with $a$ and ends with $b$ where the number of $a$'s and $b$'s are greater than zero? The notation is confusing me a little, I am new to this any help would be great thanks.

Answer 1

It means zero or more of a certain string. So $a^* = \{\emptyset,a,aa,aaa, \dots \}$ and the question wants a DFA that accepts any string of zero or more $a$'s followed by zero or more $b$'s.