Toc deterministic infinite automaton

Question

Answer 1

your initial state =n₀

let assume it as 0... while reading 'a' going to one state forward...that implies adding 1 to previous state

while reading 'b' going to one state backward... that implies decreasing 1 to  previous state...

if you have same no.of a's and b's ===> finally you are at initial position only

but you are aim is go to n₅ only.....therefore you should have exactly 5 more a's than b's to reach final state... Option : B is correct

Answer 2

Answer: B

Starting with state {0},encountering 'a' would add 1 to present state and encountering 'b' would subtract 1 from present state.Since the final state is {5} hence the accepted strings will be a^5,a^6 b,a^7 b^2,... considering an 'a' as +1 and 'b' as -1.Hence the number of a's is 5 more than b.