FOR FREE MATERIALS

Design a machine of the following language:

Answer:

As per the language given it is mod 2 and mod 3.

So, we know in this case the number of states will be 2 * 3 = 6 (total remainder pair is 6)

We design a machine for $n_{b} (ω) \mod 3 = 0 :$

And we know machine of $n_{a} (ω) \mod 2 = 0 :$

Now machine for,

Here $r_{a}$ identified remainder of a’s and $r_{b}$ identified remainder of b’s.

In the above machine, there are four grades,

So, the final state must the common state (Intersection) of $n_{b} (ω) \mod 3 = 0$ states and $n_{a} (ω) \mod 2 = 0$ .

Because language is,

$(n_{a} (ω) \mod 2 = 0) AND (n_{b} (ω) \mod 3 = 0)$ here AND means intersection.