please submit it with handwriting (Q1, b1, 4 marks, 1 for each) Find the regular expressions and Finite Automata that describe the following languages in all parts, the alphabet is {a, b}:

The language { w | |w| is odd }.

The language { w | w has an odd number of as }.

The language { w | w contains at least three as, or exactly two bs }.

The language { w | w ends in a double letter }. (A string contains a double letter if it contains aa or bb as a substring.)

(Q2, b1, 1marks, 0.5 for each) Design a FA from given regular expression

A)11 + (0 + 11)0*

B)0 (1* 01* 01*)*.

(Q3, c1, 1 marks) Analyse the following state diagram of NFAs with alphabet is {a, b}, and convert it to DFA.

Give the transition table. (0.5 mark) , Convert the NFA to DFA. (0.5 mark)

(Q4, c1, 1 marks) Analyse the following state diagram of NFAs with alphabet is {a, b}, and convert it to DFA.

Give the transition table. (0.5 mark), and design the DFA for this NFA. (0.5 mark)

(Q5, c1, 0.5 marks) Analyse the following scenario and design FA:

A simple vending machine has coffee. The price of the coffee is 50 fils. The machine accepts currency 10 fils, 20 fils only. Machine exit of the can when the amount is equal or greater than 50 fils, and do not return the remaining amount