TestBook Test Series: Theory Of Computation - Finite Automata

Question

what is the number of states in dfa of all language over {a,b} where n(a)mod3>=n(b)mod2

 

how to think in  this kind of question ??

Comments

For dfa with n(a)mod3 ..we have three states each representing mod values as 0,1,2.

Similarly for dfa with n(b)mod2 ...we have two states each representing mod values as 0,1.

So product automaton will have 6 states like {00,01,10,11,20,21} --> where first num in state represent n(a)mod3 and second num represent n(b)mod2 ..so acc to required condition n(a)mod3>=n(b)mod2...so final states in product automaton will be {00,10,11,20,21}.

Answer 1

answer is 3*2= 6

if n(a) mod x >= n(b) mod y

then no. of state is x*y

Comments

how does that work?any source or lil explanation would have helped me