Problem $2.$

a$)$ Let $=\{a,b,c,d\}.$ Draw an automaton that recognizes the language of strings where every

$"$a$"$ is followed by a $"$b$".($If you want to try this without any help, go for it$!$ For help with this

problem, see the end of this assignment.$)$

b$)$ To double check your automaton from $($a$),$ you'll want to try some test strings to make

sure it accepts and rejects the right strings. Come up with at least five test strings and note which

ones are accepted and which are rejected. As you come up with them, here are some cases you

might want to keep in mind:

Does your machine behave correctly if there is no $"$a$"$ and$/$or no $"b"$ in the test string?

$($N$.$B$.$ It's okay if there's no $"$a$"$ in the test string $-$ in that case, the condition to be in

the language is trivially true!$)$

Does your machine behave correctly if there are multiple $"$a$"$s in the test string?

Does your machine behave correctly if there are multiple $"$a$"$s or multiple $"$b$"$s in a

row?