Topic: Formal Language, Grammar and Automata

13. Let = {a,b) be an alphabet and L be the set of all strings w E * such that 1. w includes an odd number of a's and 2. for every prefix x of w, the number of b's in x is at most two more and no less than the number of a's in x Show how you construct a finite automaton M = (Q''q0F) such that L = L(M ) and describe it in a state transition diagram. 14. Let = {a,b} be an alphabet and L be the set of all strings w E such that the number of occurrences of a in w is divisible by 2 and the number of occurrences of b in w is divisible by 3. Show how you construct a finite automaton M = (Q AOF) such that L = L(M ) and describe it in a state transition diagram