MHB What are the DFA configurations for L={w:${n}_{a}$(w) mod3 < 1} on $\sum$={a,b}?

[comfortablynumb]

Find dfa's for the following language on
$\sum$={a,b};

c)
L={w:${n}_{a}$(w) mod3 < 1;

 

[Evgeny.Makarov]

You need three states $\{0,1,2\}$ that will correspond to the remainder when the number of read symbols $a$ is divided by 3. When the automaton reads a $b$, it remains in the same state. When the automaton reads an $a$, it moves to the next state. Can you figure out which states should be accepting?

 

[comfortablynumb]

Thank you, Evgeny.Makarov, I figured it out. I treated mod3<1 as mod3=0 and did it. I was okay figuring out accepting states.