Question

Automata Theory and Formal Languages

Instructions:

Draw the DFA (Deterministic Finite Automaton) of the following:

1. DFA which accepts strings of odd length
2. Design a DFA over w ∈ {a,b}^*such that number of a = 2 and there is no restriction over length of b
3. DFA for Number of a(w) mod 2 = 0 and Number of b(w) mod 2 = 0
4. DFA for Number of a(w) mod 2 = 0 orNumber of b(w) mod 2 = 0
5. DFA for Number of a(w) mod 2 != 0 andNumber of b(w) mod 2 != 0
6. DFA for Number of a(w) mod 3= 0 andNumber of b(w) mod 3= 0
7. DFA for Number of a(w) mod 3 > Number of b(w) mod 3
8. DFA for binary number divisible by 2
9. DFA for binary number divisible by 3
10. DFA in which set of all strings can be accepted which start with a
11. DFA in which set of all strings can be accepted which contains ‘a’
12. DFA in which set of all strings can be accepted which end with ‘a’
13. DFA in which set of all strings can be accepted which start with ab
14. DFA in which set of all strings can be accepted which contain ab
15. DFA in which set of all strings can be accepted which ends with ab

Answer 1

7) Soln: Keeping the enitre digram from 6 intact, just change the final states to S₁, S₅, S₂.