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Design a machine of the following language: 

L = Even number of a’s AND odd number of b’s

Answer:

As per the question,

So, language can be L = {b, aab, aba, baa, bbb, …..}

Here language is L = (mod m and mod n) then the number of states required to design the machine is m x n.

So, in that case, L = (mod 2 and mod 2) then number of states will be 2 X 2 = 4.

Here, ${\mathit{r}}_{\mathit{a}}$ identified remainder of a’s and ${\mathit{r}}_{\mathit{b}}$ identified remainder of b’s. 

In the above machine, there are four grades

1. Represent even number of  b’s
2. Represent odd number of  b’s
3. Represent even number of a’s
4. Represent odd number of a’s

Now our automata is even a’s AND odd b’s then we select the grade where we get even no. of a’s then we select the grade where we got odd no. of b’s. 

Now it is AND  means  intersection (∩) i.e. we select the final state which is common between even no. of a’s line and odd no. of b’s line.