Design a machine of the following language: 


where ∑ = {a, b}




Given language is,

So, basically, it is a mod 4 machine as follow:

Here ra identified remainder of a’s.


But as per the given language


So, the final state will be ra = 0ra = 1ra = 2.


In the exam they can ask more questions like that: 



Is it possible to get 5 as remainders (ra = 5) as we know mod 4 has maximum of 4 remainders (0 or 1 or 2 or 3) so,(na(ω) mod 4 = 5) is not possible.


So in that case what is the language?

L = ф  (no string is there which is accepted)


So what is an automata of the L = ф?

It is the automata for L = ф but it is not minimized.


It is the automata for L = ф but it is minimized.